\n| \n\n [Staggered extraction for exact matrix multiplication over every field](preprints/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026/Staggered-extraction-for-exact-matrix-multiplication-over-every-field-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"source": "OpenAI 数学仓库",
"titleEn": "Complex Matrix Multiplication Below 2.258 and Rectangular Bounds",
"abstractEnglish": "We prove that the arithmetic exponent of square matrix multiplication over every fixed field satisfies ω < 2.371054886006746. This includes every positive characteristic.",
"titleZh": "低于 2.258 的复数矩阵乘法与矩形界",
"details": {
"overview": "该研究手稿摘要声称，作者证明了在任意固定域上，方阵乘法的算术指数满足 ω < 2.371054886006746，并称该结果涵盖所有正特征情形。标题还提到“低于 2.258”和“矩形界”，但摘要未展开矩形乘法界的具体形式、证明方法或与既有结果的比较。该稿件为 AI 产生的研究手稿，收录不表示已完成独立审查或同行评议，因此上述结论应视为作者声称，尚待专业验证。",
"keyPoints": [
"稿件声称任意固定域上方阵乘法指数 ω < 2.371054886006746。",
"摘要称结果涵盖所有正特征情形。",
"标题提及低于 2.258 与矩形界，当前收录摘要未给出细节。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "59ea9c7632e6d1a7",
"section": "papers",
"category": "代数几何",
"title": "Virasoro Constraints for Projective Complete Intersections",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Virasoro conjecture for the ordinary descendant Gromov–Witten theory of smooth complete intersections in projective space, in every genus and curve class and with arbitrary cohomology insertions. This includes primitive and odd cohomology classes, with no semisimplicity assumption.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Virasoro Constraints for Projective Complete Intersections",
"titleZh": "射影完全交的Virasoro约束",
"details": {
"overview": "该稿件研究射影空间中光滑完全交的普通后代Gromov–Witten理论。作者声称证明其Virasoro猜想，覆盖每个亏格与曲线类，并允许任意上同调插入，包括本原类和奇上同调类，且不假设半单性。摘要仅陈述结论范围，未给出证明思路或技术细节；若成立，其意义在于把Virasoro约束从更受限情形推广到一般射影完全交。",
"keyPoints": [
"研究对象为射影空间光滑完全交的后代Gromov–Witten理论。",
"作者声称在每个亏格、曲线类及任意上同调插入下证明Virasoro猜想。",
"结果涵盖本原与奇上同调类，且不要求半单性假设。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "573e68ffcf7cefbc",
"section": "papers",
"category": "代数几何",
"title": "Ample rank-two bundles on the quadric surface without Griffiths-positive metrics",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We give counterexamples to Griffiths' conjecture in rank two on the quadric surface $`\\mathbb P^1\\times\\mathbb P^1`$. We construct an explicit bundle G whose coordinatewise power pullbacks, tensored with $`\\mathcal O(1,1)`$, are ample for every positive power, but admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Ample rank-two bundles on the quadric surface without Griffiths-positive metrics",
"titleZh": "二次曲面上的丰沛秩二向量丛不存在Griffiths正度量",
"details": {
"overview": "稿件在二次曲面 P^1×P^1 上给出Griffiths猜想秩二情形的反例。作者构造显式向量丛G，使其各坐标幂拉回与 O(1,1) 张量后对每个正整数幂都丰沛，但对所有充分大的幂都不存在光滑严格Griffiths正的Hermitian度量。摘要表示这构成对Griffiths猜想的反例，意义在于揭示丰沛性与Griffiths正度量之间的分离。",
"keyPoints": [
"在 P^1×P^1 上构造显式秩二向量丛G作为反例",
"G的坐标幂拉回张量 O(1,1) 对每个正幂均丰沛",
"充分大幂下不存在光滑严格Griffiths正Hermitian度量"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "568bb796335b8527",
"section": "papers",
"category": "代数几何",
"title": "Irrational cubic fourfolds with geometric K3 categories",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every sufficiently large admissible Hassett discriminant, we prove that a very general cubic fourfold of that discriminant is irrational, although its Kuznetsov component is equivalent to the ordinary derived category of a projective K3 surface. The discriminant threshold is ineffective. This disproves Kuznetsov's rationality conjecture. The same cubics have associated untwisted polarized K3 surfaces in the Hodge-theoretic sense, so they also disprove the sufficiency direction of the associated-K3 rationality prediction.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Irrational cubic fourfolds with geometric K3 categories",
"titleZh": "具有几何K3范畴的无理三次四维簇",
"details": {
"overview": "稿件研究Hassett判别式充分大的三次四维簇的有理性。作者声称对每个充分大的容许Hassett判别式，该判别式的非常一般三次四维簇不可理，尽管其Kuznetsov分量等价于某个射影K3曲面的通常导出范畴；判别式阈值非有效。摘要表示这否定Kuznetsov有理性猜想，并因这些三次簇在Hodge理论意义下对应无扭极化K3曲面，也否定关联K3有理性预测的充分性方向。",
"keyPoints": [
"对充分大容许Hassett判别式的非常一般三次四维簇证明不可理",
"其Kuznetsov分量仍等价于射影K3曲面的导出范畴",
"判别式阈值非有效，并据此否定Kuznetsov有理性猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "53b722f4947d8e25",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Brennan's conjecture and sharp inverse-square integral means",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Brennan's conjecture: if a simply connected plane domain admits a conformal bijection φ onto the unit disk, then $`|\\varphi'|^s`$ is area-integrable for every $`4/3\\lt s\\lt 4`$. We also prove the sharp inverse-square integral-means exponent $`B_{\\mathcal S}(-2)=1`$ for the normalized schlicht class $`\\mathcal S`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Brennan's conjecture and sharp inverse-square integral means",
"titleZh": "Brennan猜想与尖锐平方反比积分平均",
"details": {
"overview": "稿件研究单连通平面区域到单位圆盘的全纯双射φ的导数可积性。作者声称证明Brennan猜想：对每个 4/3 3. This is the full conjectured open range, and the threshold p = 3 is sharp.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Elliptic capacity propagation and Fourier restriction to the sphere",
"titleZh": "椭圆容量传播与球面Fourier限制",
"details": {
"overview": "稿件研究三维球面的Fourier限制猜想。作者声称证明了有界数据情形：Fourier延拓算子将L^∞(S²)有界地映入L^p(ℝ³)，对所有p>3成立；这是猜想中完整的开放范围，且阈值p=3是尖锐的。摘要未提供证明方法、技术细节或独立审查信息。",
"keyPoints": [
"证明三维球面有界数据Fourier限制猜想。",
"Fourier延拓算子将L^∞(S²)有界映入L^p(ℝ³)，对所有p>3。",
"阈值p=3尖锐，覆盖猜想中完整开放范围。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数论与算术几何",
"interest": []
},
{
"id": "3cc55032de38d32c",
"section": "papers",
"category": "动力系统与遍历论",
"title": "Continuous Phase Foliations Create Analytic Caustic Collars",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Continuous-Phase-Foliations-Create-Analytic-Caustic-Collars-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For a smooth strictly convex planar billiard of positive curvature, a continuous foliation of a full grazing annulus by individually invariant essential curves forces an analytic boundary and a jointly analytic collar of smooth strictly convex caustics. The physical-collar rigidity theorem proved in the companion article then implies that the table is an ellipse.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Continuous Phase Foliations Create Analytic Caustic Collars",
"titleZh": "连续相位叶状结构产生解析焦散领",
"details": {
"overview": "稿件研究光滑严格凸正曲率平面台球的掠射环带。作者声称，若一个满掠射环带被连续叶状结构划分为各自不变的本质曲线，则边界必为解析的，并存在光滑严格凸焦散的联合解析领。结合伴随文章的物理领刚性定理，可推出台球桌为椭圆。当前收录摘要未给出证明细节或独立审查信息。",
"keyPoints": [
"研究正曲率严格凸平面台球掠射环带的连续不变叶状结构。",
"该结构迫使边界解析并产生联合解析的焦散领。",
"结合伴随文章的刚性定理推出台球桌为椭圆。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "3cb12aea6200969b",
"section": "papers",
"category": "分析与偏微分方程",
"title": "A strict inverse-first-power bound for univalent functions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove a uniform upper bound for inverse-first-power integral means of normalized univalent disk maps with exponent strictly below 1/4. Consequently, the bounded universal integral-means spectrum satisfies $`B_b(-1)\\lt 1/4`$, disproving Kraetzer's conjectured spectrum at p = −1.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A strict inverse-first-power bound for univalent functions",
"titleZh": "单叶函数的严格逆一次幂界",
"details": {
"overview": "稿件研究归一化单叶圆盘映射的逆一次幂积分平均。作者声称，对指数严格小于1/4的情形证明了统一上界；由此有界通用积分平均谱满足B_b(-1)<1/4，从而在p=−1处否定了Kraetzer猜想的谱。当前收录摘要未给出证明细节或独立验证信息。",
"keyPoints": [
"对指数严格小于1/4的逆一次幂积分平均证明统一上界。",
"推出有界通用积分平均谱满足B_b(-1)<1/4。",
"在p=−1处否定Kraetzer猜想的谱。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "3b9c4a6bc3964f66",
"section": "papers",
"category": "数学物理与量子信息",
"title": "The periodic spin-one Haldane gap",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove a uniform positive spectral gap for the pure antiferromagnetic spin-one Heisenberg chain on even periodic rings, establishing the positive even-periodic formulation of the spin-one Haldane conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The periodic spin-one Haldane gap",
"titleZh": "周期自旋一Haldane能隙",
"details": {
"overview": "稿件研究偶数周期环上纯反铁磁自旋一Heisenberg链的谱隙。作者声称证明了均匀正谱隙，从而建立自旋一Haldane猜想的正偶数周期表述。当前收录摘要未给出证明方法、技术细节或独立审查信息。",
"keyPoints": [
"研究偶数周期环上纯反铁磁自旋一Heisenberg链。",
"证明存在均匀正谱隙。",
"建立自旋一Haldane猜想的正偶数周期表述。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "3b7c08de3140c91a",
"section": "papers",
"category": "几何与拓扑",
"title": "Path selection and an elliptic inequality on degenerating Ricci-flat trees",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Path-selection-and-an-elliptic-inequality-on-degenerating-Ricci-flat-trees-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove a sequential elliptic inequality for the renormalized Einstein–Hilbert functional on a fixed finite tree of four-dimensional Ricci-flat spaces. As the joining lengths diverge and the scale-neutral weighted Ricci error M tends to zero, the functional satisfies $`E=o(M)`$. The root end has decay exponent greater than one, and every joined quotient group is nontrivial. We also prove the multivariable path-selection theorem for asymptotic expansions used to obtain this estimate.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Path selection and an elliptic inequality on degenerating Ricci-flat trees",
"titleZh": "退化Ricci平坦树上的路径选择与一个椭圆不等式",
"details": {
"overview": "稿件研究固定有限棵四维Ricci平坦空间构成的树上的重整化Einstein–Hilbert泛函。作者声称：当连接长度发散、尺度中性加权Ricci误差M趋于零时，该泛函满足E=o(M)；根端衰减指数大于一，且每个拼接商群非平凡。摘要还表示证明了用于得到该估计的多变量路径选择定理。研究意义在于为退化几何上的泛函渐近控制提供工具，但结果尚未经独立审查。",
"keyPoints": [
"在固定有限四维Ricci平坦空间树上证明重整化Einstein–Hilbert泛函的序列椭圆不等式",
"当连接长度发散且加权Ricci误差M趋零时，泛函满足E=o(M)",
"根端衰减指数大于一，每个拼接商群非平凡；另证多变量路径选择定理"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "微分几何",
"interest": []
},
{
"id": "3afa90a7784e1529",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.158.0-alpha.5 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.158.0-alpha.5",
"date": "2026-09-24",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-23T22:10:20+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.158.0-alpha.5 测试版发布",
"details": {
"overview": "Codex CLI 0.158.0-alpha.5 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "3a76ffbbf057a799",
"section": "papers",
"category": "概率与统计",
"title": "A typical-start upper bound for low-temperature SK Glauber dynamics",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-typical-start-upper-bound-for-low-temperature-SK-Glauber-dynamics-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed inverse temperature β > 1, we prove subexponential mixing for rate-one-per-site heat-bath dynamics in the zero-field Gaussian Sherrington–Kirkpatrick model from a typical equilibrium configuration. If one Gibbs-sampled configuration is held fixed as the initial state, its total-variation distance from equilibrium is at most 1/4 by time $`\\exp(n^{1-1/40000000})`$, with joint probability tending to one over the disorder and the sampled state.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A typical-start upper bound for low-temperature SK Glauber dynamics",
"titleZh": "低温SK Glauber动力学的典型初态上界",
"details": {
"overview": "稿件研究零场高斯Sherrington–Kirkpatrick模型在每格点速率为一的热浴动力学。作者声称：对每个固定逆温度β>1，从典型平衡构型出发具有次指数混合；若固定一个Gibbs采样构型作为初态，则到时间exp(n^{1-1/40000000})时其与平衡的全变差距离至多1/4，且该结论在无序与采样态上的联合概率趋于一。摘要给出的是典型初态下的混合上界，尚未经独立验证。",
"keyPoints": [
"研究零场高斯SK模型每格点速率一的热浴动力学在固定β>1时的混合行为",
"声称从典型平衡构型出发达到次指数混合",
"固定Gibbs采样初态时，至时间exp(n^{1-1/40000000})全变差距离至多1/4，联合概率趋一"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与随机过程",
"interest": []
},
{
"id": "3a18f94e36def873",
"section": "papers",
"category": "组合数学与图论",
"title": "Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Sharp-Logarithmic-Exponents-for-Fixed-Off-Diagonal-Ramsey-Numbers-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed integer s ≥ 6, we determine the sharp logarithmic exponent of the off-diagonal Ramsey number:\n\n$`\\displaystyle r(s,t)=\\frac{t^{s-1}}{(\\log t)^{s-2+o(1)}} \\qquad (t\\longrightarrow\\infty).`$",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers",
"titleZh": "固定非对角Ramsey数的精确对数指数",
"details": {
"overview": "稿件研究非对角Ramsey数r(s,t)在s固定、t趋于无穷时的渐近阶。作者声称：对每个固定整数s≥6，确定了精确的对数指数，即r(s,t)=t^{s-1}/(log t)^{s-2+o(1)}。该结果刻画了分母中对数因子的幂次，属于极值组合中的经典渐近问题；当前收录摘要未给出证明细节，且稿件尚未经独立审查或同行评议。",
"keyPoints": [
"研究对象为固定s≥6、t趋于无穷时的非对角Ramsey数r(s,t)",
"作者声称确定精确对数指数：r(s,t)=t^{s-1}/(log t)^{s-2+o(1)}",
"结果刻画分母对数因子的幂次，属极值组合渐近问题"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "37deb6fbc5fc33bd",
"section": "papers",
"category": "代数与表示论",
"title": "Tensor saturation for even spin groups",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the saturation conjecture for $`\\mathop{\\mathrm{Spin}}\\nolimits (2n)`$, n ≥ 2. If three dominant integral weights sum to an element of the root lattice, then the existence of a nonzero tensor invariant after a positive integral dilation implies the existence of one at the original weights.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Tensor saturation for even spin groups",
"titleZh": "偶自旋群的张量饱和性",
"details": {
"overview": "稿件研究偶自旋群Spin(2n)（n≥2）的张量饱和猜想。作者声称证明了该猜想：若三个支配整权之和属于根格，则经过某个正整数倍膨胀后存在非零张量不变量，蕴含原权重处也存在非零张量不变量。该结论涉及表示论中张量不变量存在性的饱和现象，摘要仅给出陈述，未展开证明，且稿件尚未经独立审查。",
"keyPoints": [
"研究对象为偶自旋群Spin(2n)，n≥2，及其张量不变量",
"作者声称证明饱和猜想：三支配整权之和属根格时，正整倍膨胀下有不变量则原权重处也有",
"结论属表示论中张量不变量存在性的饱和现象"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "表示论",
"interest": []
},
{
"id": "37d592f4d3c59488",
"section": "papers",
"category": "数学物理与量子信息",
"title": "A radial continuum phase transition with algebraic decay",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a bounded, continuous, stable radial pair potential in three dimensions with $`|\\phi(r)|\\le Cr^{-3-1/32}`$ for r ≥ 1. Throughout an open interval of positive densities, its canonical thermodynamic free energy is finite at every positive inverse temperature and has a strict downward derivative jump at one common finite positive inverse temperature.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A radial continuum phase transition with algebraic decay",
"titleZh": "具有代数衰减的径向连续相变",
"details": {
"overview": "稿件在三维空间构造一个有界、连续、稳定的径向对势，满足r≥1时|φ(r)|≤Cr^{-3-1/32}。作者声称：在一个正密度的开区间上，其正则热力学自由能在每个正逆温度处有限，并在某个共同有限正逆温度处出现严格向下的导数跳跃。这给出代数衰减势下径向连续相变的例子，摘要未提供证明细节，结果尚待独立审查。",
"keyPoints": [
"在三维构造有界连续稳定径向对势，满足|φ(r)|≤Cr^{-3-1/32}（r≥1）",
"声称正密度开区间上正则自由能在每个正逆温度有限",
"在共同有限正逆温度处出现严格向下的导数跳跃"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理",
"interest": []
},
{
"id": "349033f0ca45ec9c",
"section": "papers",
"category": "几何与拓扑",
"title": "The affine Bernstein theorem in dimensions three through nine",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-affine-Bernstein-theorem-in-dimensions-three-through-nine-September-24-2026/main.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Euclidean-complete affine Bernstein conjecture in dimensions three through nine: a smooth locally uniformly convex affine maximal graph is an elliptic paraboloid whenever its induced Euclidean metric is complete. The same conclusion holds, without an initial graph assumption, for connected smooth open (noncompact and without boundary) affine-complete locally uniformly convex immersed hypersurfaces that are classically affine maximal in these dimensions.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The affine Bernstein theorem in dimensions three through nine",
"titleZh": "三至九维的仿射Bernstein定理",
"details": {
"overview": "稿件研究仿射Bernstein猜想。作者声称在三维至九维证明欧氏完备情形：若光滑局部一致凸仿射极大图诱导的欧氏度量完备，则该图是椭圆抛物面。摘要还表示，在这些维数中，对连通光滑开（非紧无边界）仿射完备、局部一致凸且经典仿射极大的浸入超曲面，无需初始图假设也得到同一结论。该结果属仿射微分几何，尚未经独立审查。",
"keyPoints": [
"在三维至九维证明欧氏完备仿射Bernstein猜想",
"光滑局部一致凸仿射极大图若诱导欧氏度量完备，则为椭圆抛物面",
"对仿射完备局部一致凸经典仿射极大浸入超曲面，无需图假设得同一结论"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "微分几何",
"interest": []
},
{
"id": "32fe2cb0a7bca47e",
"section": "papers",
"category": "代数几何",
"title": "Symmetry of semialgebraic bounded domains with compact quotient",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every nonempty connected semialgebraic bounded open subset of a complex affine variety admitting a properly discontinuous cocompact group of biholomorphisms is smooth and biholomorphic to a bounded symmetric domain. This answers the bounded-domain question of Kollár and Pardon affirmatively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Symmetry of semialgebraic bounded domains with compact quotient",
"titleZh": "具有紧商的全纯有界域的半代数对称性",
"details": {
"overview": "稿件研究复仿射簇中非空连通半代数有界开子集，假设其容许一个真不连续且余紧的双全纯群作用。作者声称：此类域必光滑，且双全纯于有界对称域，从而正面回答Kollár与Pardon提出的有界域问题。该结论联系半代数几何、双全纯群作用与对称域分类，当前收录摘要未给出证明细节，稿件尚未经独立审查。",
"keyPoints": [
"研究对象为复仿射簇中容许真不连续余紧双全纯群的半代数有界开集",
"作者声称此类域必光滑且双全纯于有界对称域",
"正面回答Kollár与Pardon的有界域问题"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "复几何",
"interest": []
},
{
"id": "3224c04a8ddc8fd9",
"section": "papers",
"category": "代数几何",
"title": "P=W in composite rank for fixed determinant",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the P = W conjecture on the full rational cohomology of fixed-determinant, trace-free Higgs moduli spaces in composite rank and coprime degree, for smooth projective complex curves of genus at least two. Together with the established prime-rank cases, this gives the equality in every coprime rank.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "P=W in composite rank for fixed determinant",
"titleZh": "固定行列式下合数秩的P=W",
"details": {
"overview": "稿件研究亏格至少二的平滑射影复曲线上固定行列式、无迹Higgs模空间的全有理上同调。作者声称在合数秩且度互素情形证明P=W猜想；结合已确立的素数秩情形，得到所有互素秩下的等式。该结果涉及Higgs丛模空间与非阿贝尔Hodge理论中的P=W对应，摘要仅给出陈述，尚未经独立审查或同行评议。",
"keyPoints": [
"研究对象为亏格≥2平滑射影复曲线上固定行列式无迹Higgs模空间的全有理上同调",
"作者声称在合数秩且度互素时证明P=W猜想",
"结合素数秩情形，声称所有互素秩下等式成立"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "31cdcdee04611260",
"section": "papers",
"category": "分析与偏微分方程",
"title": "The critical dimension for one-phase Bernoulli minimizers",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that seven is the critical dimension for the one-phase Bernoulli problem: every nonzero one-homogeneous global minimizer in dimensions at most six is flat, while a nonflat one-homogeneous global minimizer exists in dimension seven. It follows that the interior free boundary of a local minimizer is smooth in dimensions at most six. In dimension n ≥ 7, its singular set has Hausdorff dimension at most $`n-7`$, and this bound is sharp. In dimension seven, the singular set is locally finite.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The critical dimension for one-phase Bernoulli minimizers",
"titleZh": "单相Bernoulli极小元的临界维数",
"details": {
"overview": "稿件研究单相Bernoulli问题的临界维数。作者声称七是临界维数：维数至多六时，每个非零一阶齐次全局极小元是平坦的；维数七存在非平坦一阶齐次全局极小元。由此，局部极小元内部自由边界在维数至多六时光滑；n≥7时奇异集Hausdorff维数至多n-7且界是 sharp 的；维数七奇异集局部有限。摘要未展开证明，结果尚待独立审查。",
"keyPoints": [
"作者声称七是单相Bernoulli问题的临界维数",
"维数≤6时非零一阶齐次全局极小元平坦，维数7存在非平坦例子",
"n≥7时奇异集Hausdorff维数至多n-7且 sharp；维数7奇异集局部有限"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "偏微分方程",
"interest": []
},
{
"id": "317a844fec18ad54",
"section": "papers",
"category": "几何与拓扑",
"title": "A marked tensor obstruction to four-dimensional disk embedding",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-marked-tensor-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove the unrestricted four-dimensional disk-embedding conjecture. We construct immersed disks in a compact oriented smooth four-manifold with framed algebraic dual spheres satisfying the usual equivariant intersection and reduced self-intersection conditions, but with no pairwise disjoint locally flat replacements that preserve the boundary maps and induced normal framings. The obstruction holds even when the replacement disks' relative homotopy classes are not prescribed.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A marked tensor obstruction to four-dimensional disk embedding",
"titleZh": "四维圆盘嵌入的一个带标记张量障碍",
"details": {
"overview": "稿件研究四维圆盘嵌入猜想。作者声称否定无限制版本：在紧致有向光滑四维流形中构造浸入圆盘，配有标架代数对偶球，满足通常等变相交与约化自交条件，但不存在两两不交的局部平坦替换圆盘同时保持边界映射与诱导法标架；即使不规定替换圆盘的相对同伦类，障碍仍成立。当前收录摘要未给出证明细节，稿件尚未经独立审查。",
"keyPoints": [
"作者声称否定无限制的四维圆盘嵌入猜想",
"构造满足等变相交与约化自交条件的浸入圆盘及标架代数对偶球",
"不存在保持边界映射与诱导法标架的两两不交局部平坦替换；不规定相对同伦类仍有障碍"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何拓扑",
"interest": []
},
{
"id": "302ffd48e9935ad4",
"section": "papers",
"category": "概率与统计",
"title": "Hellinger contraction with arbitrary Boolean output bias",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Hellinger-contraction-with-arbitrary-Boolean-output-bias-September-24-2026/main.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Hellinger conjecture for Boolean functions on the uniform discrete cube, with arbitrary output bias. For a Boolean function of mean m and every $`\\rho\\in[-1,1]`$, the loss $`\\sqrt{1-m^2}-\\mathbb E\\sqrt{1-(T_\\rho f)^2}`$ is at most $`1-\\sqrt{1-\\rho^2}`$, with equality for signed coordinates. The proof combines asymmetric dimension induction, a calibrated noise-semigroup energy estimate, and finite exact arithmetic certificates. The Hellinger inequality also yields the Courtade–Kumar information bound.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Hellinger contraction with arbitrary Boolean output bias",
"titleZh": "任意布尔输出偏置下的Hellinger收缩",
"details": {
"overview": "稿件研究均匀离散立方体上布尔函数的Hellinger猜想，允许任意输出偏置。作者声称：对均值m的布尔函数及每个ρ∈[-1,1]，损失√(1-m²)-E√(1-(T_ρf)²)至多1-√(1-ρ²)，符号坐标取等。证明结合非对称维数归纳、校准噪声半群能量估计与有限精确算术证书；该不等式还推出Courtade–Kumar信息界。摘要未展开细节，结果尚待独立审查。",
"keyPoints": [
"研究均匀离散立方体上布尔函数在任意输出偏置下的Hellinger猜想",
"声称损失√(1-m²)-E√(1-(T_ρf)²)≤1-√(1-ρ²)，符号坐标取等",
"证明结合非对称维数归纳、噪声半群能量估计与有限精确算术证书；推出Courtade–Kumar信息界"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "理论计算机科学",
"interest": []
},
{
"id": "2f25c962aa5901dd",
"section": "papers",
"category": "优化与控制",
"title": "The approximation threshold for metric k-median",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Approximation-Threshold-for-Metric-k-Median-September-24-2026/main.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed ε > 0, we give a deterministic polynomial-time $`(1+2/e+\\varepsilon)`$-approximation for finite rational metric k-median with specified candidate facilities, opening at most k facilities. Under $`P\\ne NP`$, the infimum approximation factor in this model is therefore $`1+2/e`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The approximation threshold for metric k-median",
"titleZh": "度量k-中位问题的近似阈值",
"details": {
"overview": "稿件研究带指定候选设施、至多开设k个设施的有限有理度量k-中位问题。作者声称：对每个固定ε>0，给出确定性多项式时间(1+2/e+ε)-近似算法；因此在P≠NP下，该模型中的近似因子下确界为1+2/e。该结果刻画了该模型的可近似阈值，当前收录摘要未给出算法与下界证明细节，稿件尚未经独立审查。",
"keyPoints": [
"研究对象为带指定候选设施、至多开设k个设施的有限有理度量k-中位",
"作者声称对每个固定ε>0给出确定性多项式时间(1+2/e+ε)-近似",
"在P≠NP下，该模型近似因子下确界为1+2/e"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算法与复杂性",
"interest": []
},
{
"id": "2eecdb71425efffa",
"section": "papers",
"category": "代数几何",
"title": "Minimal models in numerical dimension one",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If KX is pseudo-effective and $`\\kappa_\\sigma(X,K_X)=1`$, with κσ defined by section growth with a fixed ample twist, then X admits a projective ℚ-factorial terminal minimal model.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Minimal models in numerical dimension one",
"titleZh": "数值维数一中的极小模型",
"details": {
"overview": "稿件研究光滑连通复射影簇（维数至少三）的极小模型猜想中数值维数为一的情形。摘要表示，若KX伪有效且κσ(X,KX)=1（κσ由固定丰沛扭曲下的截面增长定义），则X存在射影ℚ-分解终端极小模型。该结果针对极小模型纲领中的边界情形，作者声称解决了该特定情形；材料未说明证明方法或与其他工作的关系。",
"keyPoints": [
"研究对象为维数至少三的光滑连通复射影簇。",
"在KX伪有效且κσ=1条件下声称存在射影ℚ-分解终端极小模型。",
"κσ由固定丰沛扭曲下的截面增长定义。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "2ccd55321a52477d",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.158.0-alpha.7 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.158.0-alpha.7",
"date": "2026-09-24",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-24T05:28:27+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.158.0-alpha.7 测试版发布",
"details": {
"overview": "Codex CLI 0.158.0-alpha.7 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "2cb0a498725f8dd3",
"section": "papers",
"category": "概率与统计",
"title": "The free energy of the Ising random perceptron",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-free-energy-of-the-Ising-random-perceptron-September-24-2026/The-free-energy-of-the-Ising-random-perceptron-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We determine the limiting free energy of the Ising perceptron with independent Gaussian patterns for every bounded Borel log-potential, at every fixed positive temperature and pattern density. We give an explicit variational formula for the limit and prove convergence in expectation and probability.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The free energy of the Ising random perceptron",
"titleZh": "Ising随机感知机的自由能",
"details": {
"overview": "稿件研究具有独立高斯模式的Ising感知机模型，摘要声称对任意有界Borel对数势、每个固定正温度和模式密度，确定了极限自由能。作者给出极限的显式变分公式，并证明依期望和依概率收敛。该结果属于随机感知机与统计物理交叉的概率分析，材料未涉及具体证明技术或与已有结果的比较。",
"keyPoints": [
"研究对象为独立高斯模式下的Ising感知机。",
"对任意有界Borel对数势给出极限自由能的显式变分公式。",
"证明在固定正温度和模式密度下依期望与依概率收敛。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论",
"interest": []
},
{
"id": "27af8d236d21c45f",
"section": "papers",
"category": "代数几何",
"title": "The normalized-volume gap in dimension four",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every singular complex algebraic klt fourfold germ with zero boundary has normalized volume at most 162, with equality precisely for an analytic ordinary double point. This resolves the ordinary-double-point volume-gap conjecture in dimension four.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The normalized-volume gap in dimension four",
"titleZh": "四维中的正规化体积间隙",
"details": {
"overview": "稿件研究四维中边界为零的奇异复代数klt芽。摘要声称证明其正规化体积至多为162，且等号恰在解析普通二重点处取得，从而解决四维的普通二重点体积间隙猜想。该结果涉及极小模型纲领中的体积不变量与奇点分类；材料未给出证明思路、构造细节或独立验证信息。",
"keyPoints": [
"对象为四维零边界奇异复代数klt芽。",
"声称正规化体积上界为162，等号仅在解析普通二重点取得。",
"据此声称解决四维普通二重点体积间隙猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "26205f4696a2f04c",
"section": "papers",
"category": "概率与统计",
"title": "The free energy of the spherical random perceptron",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-free-energy-of-the-spherical-random-perceptron-September-24-2026/The-free-energy-of-the-spherical-random-perceptron-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove an exact variational formula for the limiting pressure of the spherical random perceptron with an arbitrary bounded continuous single-pattern potential. The formula holds at every fixed positive density and inverse temperature, with convergence in expectation and in probability.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The free energy of the spherical random perceptron",
"titleZh": "球面随机感知机的自由能",
"details": {
"overview": "稿件研究球面随机感知机模型，摘要声称对任意有界连续单模式势，证明了极限压力的精确变分公式。该公式在每个固定正密度和逆温度下成立，并具有依期望与依概率收敛。研究属于随机感知机与统计物理的概率分析；材料未说明证明方法、模型参数范围之外的假设或与已有文献的关系。",
"keyPoints": [
"研究对象为带任意有界连续单模式势的球面随机感知机。",
"给出极限压力的精确变分公式。",
"在固定正密度和逆温度下证明依期望与依概率收敛。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论",
"interest": []
},
{
"id": "245ca8a17f16806f",
"section": "papers",
"category": "理论计算机科学",
"title": "An Almost-Linear Approximation Scheme for Edit Distance",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We give a uniform randomized approximation scheme for unit-cost edit distance. For every fixed rational $`\\varepsilon\\in(0,1)`$, it estimates the distance between arbitrary explicitly stored strings of total length N within a factor $`1+\\varepsilon`$ with probability at least 2/3, in worst-case expected time $`N^{1+o(1)}`$ on a logarithmic-word RAM. The algorithm supports polynomially bounded integer alphabets and returns zero deterministically on equal strings.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An Almost-Linear Approximation Scheme for Edit Distance",
"titleZh": "编辑距离的近似线性时间近似方案",
"details": {
"overview": "稿件研究单位代价编辑距离的近似计算。摘要声称对每个固定有理数ε∈(0,1)，可在对数词RAM上以最坏情形期望时间N^{1+o(1)}，以至少2/3的概率给出总长N的任意显式存储字符串间距离的1+ε近似。算法支持多项式有界整数字母表，并在字符串相等时确定性返回零。该结果属于字符串算法与细粒度复杂度方向；材料未给出技术细节或实验评估。",
"keyPoints": [
"对固定ε给出单位代价编辑距离的1+ε随机近似方案。",
"最坏情形期望时间为N^{1+o(1)}，成功概率至少2/3。",
"支持多项式有界整数字母表，相等字符串确定性返回零。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算法与复杂度",
"interest": []
},
{
"id": "22903ee7a92b34e7",
"section": "papers",
"category": "数学物理与量子信息",
"title": "A continuum temperature singularity for a radial pair potential",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a stable radial pair potential in three dimensions whose canonical free energy has a strict downward derivative jump at one common finite positive inverse temperature throughout an open interval of positive densities. The potential has a divergent repulsive core, a nontrivial attractive interval, and an integrable tail satisfying $`\\phi(r)=o(r^{-3})`$. Its free-cube canonical free energy is finite at every positive inverse temperature and density.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A continuum temperature singularity for a radial pair potential",
"titleZh": "径向对势的连续温度奇异性",
"details": {
"overview": "稿件研究三维中稳定径向对势的规范自由能。摘要声称构造了一个势，使规范自由能在某个共同有限正逆温度处、沿一个正密度开区间出现严格向下的导数跳跃。该势具有发散排斥核、非平凡吸引区间及满足φ(r)=o(r^{-3})的可积尾部，且自由立方体规范自由能在每个正逆温度和密度下有限。研究属于数学统计物理；材料未说明构造方法或物理解释。",
"keyPoints": [
"构造三维稳定径向对势，其规范自由能在共同逆温度处出现导数跳跃。",
"势具有发散排斥核、非平凡吸引区间和可积尾部φ(r)=o(r^{-3})。",
"自由立方体规范自由能在所有正逆温度和密度下有限。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理",
"interest": []
},
{
"id": "21fbfeef19f23b9b",
"section": "papers",
"category": "动力系统与遍历论",
"title": "Two limit cycles for quintic Liénard systems",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/two-limit-cycles-for-quintic-lienard-systems-September-24-2026/two-limit-cycles-for-quintic-lienard-systems-September-24-2026.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every classical Liénard system $`\\dot x=y-F(x)`$, $`\\dot y=-x`$, with F an arbitrary real polynomial of degree at most five, has at most two geometrically distinct isolated periodic orbits, and the bound is attained. This proves the degree-five case of the Lins Neto–de Melo–Pugh conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Two limit cycles for quintic Liénard systems",
"titleZh": "五次Liénard系统的两个极限环",
"details": {
"overview": "稿件研究经典Liénard系统ẋ=y−F(x)、ẏ=−x，其中F为次数至多五的任意实多项式。摘要声称该系统至多有两个几何不同的孤立周期轨道，且该上界可达，从而证明Lins Neto–de Melo–Pugh猜想的五次情形。研究属于常微分方程极限环理论；材料未说明证明策略或与低次情形的比较。",
"keyPoints": [
"研究对象为F次数至多五的经典Liénard系统。",
"声称至多有两个几何不同的孤立周期轨道且上界可达。",
"据此证明Lins Neto–de Melo–Pugh猜想的五次情形。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "常微分方程与动力系统",
"interest": []
},
{
"id": "20e6db56826336a4",
"section": "papers",
"category": "组合数学与图论",
"title": "The sharp logarithmic exponent of r(5,t)",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Sharp-Logarithmic-Exponent-of-r-5-t-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We determine the sharp logarithmic exponent of the off-diagonal Ramsey number $`r(5,t)`$:\n\n$`\\displaystyle r(5,t)=\\frac{t^4}{(\\log t)^{3+o(1)}} \\qquad (t\\longrightarrow\\infty).`$",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The sharp logarithmic exponent of r(5,t)",
"titleZh": "r(5,t)的精确对数指数",
"details": {
"overview": "稿件研究非对角Ramsey数r(5,t)的渐近行为。摘要声称确定了其精确对数指数，即当t趋于无穷时r(5,t)=t^4/(log t)^{3+o(1)}。该结果刻画了r(5,t)在t^4量级下对数因子的幂次；材料未给出证明方法、上下界构造细节或独立验证信息。",
"keyPoints": [
"研究对象为非对角Ramsey数r(5,t)的渐近阶。",
"声称r(5,t)=t^4/(log t)^{3+o(1)}当t趋于无穷。",
"确定了对数因子的精确指数3。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "204a3298490364df",
"section": "papers",
"category": "代数与表示论",
"title": "The equivariant cohomological Hikita conjecture for arbitrary quivers",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the equivariant cohomological Hikita conjecture for arbitrary finite quivers, including loops and multiple arrows. For any dimension and framing vectors, any commuting flavor torus, and a stability character whose semistable locus is stable and has free gauge action, the equivariant cohomology of the Nakajima variety is canonically isomorphic to the coordinate ring of the scheme-theoretic fixed locus of the stability cocharacter on the flavor-deformed Coulomb branch. This is an isomorphism of graded algebras over the common coefficient ring, retaining nilpotents and including the empty case.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The equivariant cohomological Hikita conjecture for arbitrary quivers",
"titleZh": "任意箭图的等变上同调Hikita猜想",
"details": {
"overview": "稿件研究任意有限箭图（含环与多重箭）的等变上同调Hikita猜想。摘要声称对任意维数与框架向量、任意交换flavor环面，以及半稳定轨迹稳定且规范作用自由的稳定性特征，Nakajima簇的等变上同调与flavor形变Coulomb分支上稳定性余特征簇理论不动点的坐标环典范同构。该同构为共同系数环上的分次代数同构，保留幂零元并包含空情形。",
"keyPoints": [
"对含环和多重箭的任意有限箭图证明等变上同调Hikita猜想。",
"在同构中保留幂零元，并覆盖空情形。",
"同构为共同系数环上的分次代数同构。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "1e89ea4a783ace99",
"section": "papers",
"category": "数学物理与量子信息",
"title": "Spontaneous magnetization in the quantum Heisenberg ferromagnet",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every dimension d ≥ 3 and every spin $`S\\in\\{\\frac12,1,\\frac32,\\ldots\\}`$, we prove that the nearest-neighbor isotropic quantum Heisenberg ferromagnet has a translation-invariant, spontaneously magnetized equilibrium state at every sufficiently low positive temperature. The same state satisfies the KMS condition for the zero-field dynamics and has magnetization at least $`S/4`$. This resolves the low-temperature ordering problem in the spontaneous-magnetization formulation.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Spontaneous magnetization in the quantum Heisenberg ferromagnet",
"titleZh": "量子Heisenberg铁磁体中的自发磁化",
"details": {
"overview": "稿件研究最近邻各向同性量子Heisenberg铁磁体。摘要声称对每个维数d≥3和每个自旋S∈{1/2,1,3/2,…}，在充分低的正温度下存在平移不变且自发磁化的平衡态；该态满足零场动力学的KMS条件，磁化强度至少为S/4。作者称这解决了自发磁化表述下的低温有序问题。研究属于数学物理；材料未说明证明方法或模型推广。",
"keyPoints": [
"对d≥3和任意半整数自旋S，声称存在自发磁化平衡态。",
"该态平移不变、满足KMS条件，磁化强度至少S/4。",
"声称解决自发磁化表述下的低温有序问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理",
"interest": []
},
{
"id": "1e087e47b09e4cf3",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Endpoint pointwise convergence for the Schrodinger equation in higher dimensions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the Sobolev endpoint of Carleson's pointwise convergence problem in every dimension n ≥ 3. For initial data in $`H^{n/(2(n+1))}(\\mathbb R^n)`$, the free Schrödinger evolution converges almost everywhere to the initial data as $`t\\downarrow0`$. The evolution is defined by removing Gaussian regularization on one full-measure spatial set, uniformly over the interval $`0\\lt t\\lt 1`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Endpoint pointwise convergence for the Schrodinger equation in higher dimensions",
"titleZh": "高维Schrödinger方程端点逐点收敛",
"details": {
"overview": "稿件研究Carleson逐点收敛问题在维数n≥3时的Sobolev端点。摘要声称对初值属于H^{n/(2(n+1))}(ℝ^n)，自由Schrödinger演化当t↓0时几乎处处收敛到初值。演化通过在一个满测度空间集上移除Gaussian正则化定义，并在0 0 and C < ∞ such that every set $`A\\subseteq\\{1,\\ldots,N\\}`$ with no nonzero square difference satisfies $`|A|\\le C N^{1-c}`$. This answers the fixed-power question posed by Green and Sawhney.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A power saving for square-difference-free sets",
"titleZh": "无平方差集合的幂次节省",
"details": {
"overview": "该稿件研究整数区间{1,…,N}中不含非零平方差的集合大小。作者声称证明存在绝对常数c>0与C<∞，使每个此类集合满足|A|≤C N^{1−c}，从而回答Green与Sawhney提出的固定幂次问题。若成立，将给出无平方差集合上界从次多项式型改进到固定幂次节省的定量结果。",
"keyPoints": [
"研究对象为{1,…,N}中不含非零平方差的集合。",
"作者声称证明|A|≤C N^{1−c}，其中c>0、C<∞为绝对常数。",
"称该结果回答Green与Sawhney的固定幂次问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "01e75fc23319ca23",
"section": "papers",
"category": "数学物理与量子信息",
"title": "Generalized outer-electron radii of neutral Coulomb atoms",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the radius part of the generalized ionization conjecture for neutral nonrelativistic Coulomb atoms with two spin states. For every choice of ground states, the upper and lower large-nuclear-charge limits of the radius defined by an expected exterior electron mass m are both asymptotic to $`(81\\pi^2/2)^{1/3}m^{-1/3}`$ as m tends to infinity.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Generalized outer-electron radii of neutral Coulomb atoms",
"titleZh": "中性库仑原子的广义外电子半径",
"details": {
"overview": "该稿件研究具有两个自旋态的中性非相对论库仑原子的广义电离猜想中的半径部分。作者声称对任意基态选择，由期望外部电子质量m定义的半径，其大核电荷数上下极限在m趋于无穷时均渐近于(81π²/2)^{1/3}m^{−1/3}。若成立，将为该半径在质量参数大极限下的精确渐近行为提供数学依据。",
"keyPoints": [
"研究双自旋态中性非相对论库仑原子的广义电离猜想半径部分。",
"作者声称对任意基态选择，半径的大核电荷上下极限相同。",
"该极限渐近为(81π²/2)^{1/3}m^{−1/3}，当m趋于无穷。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "018bcc32d96c690c",
"section": "papers",
"category": "代数几何",
"title": "Semialgebraic universal covers of normal projective varieties",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf",
"date": "2026-09-24",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Kollár–Pardon conjecture: the universal cover of a connected normal projective complex variety is biholomorphic to a semialgebraic open subset of a projective variety if and only if it is a product of a bounded symmetric domain, a complex affine space, and a simply connected normal projective variety.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Semialgebraic universal covers of normal projective varieties",
"titleZh": "正规射影簇的半代数万有覆盖",
"details": {
"overview": "该稿件研究连通正规射影复簇的万有覆盖。作者声称证明Kollár–Pardon猜想：万有覆盖双全纯于某个射影簇的半代数开子集，当且仅当它是有界对称域、复仿射空间与单连通正规射影簇的乘积。若成立，将刻画这类万有覆盖的半代数性，并给出其结构分解。",
"keyPoints": [
"研究连通正规射影复簇万有覆盖的半代数性。",
"作者声称证明Kollár–Pardon猜想，给出双全纯等价条件。",
"结构分解为有界对称域、复仿射空间与单连通正规射影簇之积。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "ff9438e4483571d5",
"section": "papers",
"category": "组合数学与图论",
"title": "A power saving for planar unit distances",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-power-saving-for-planar-unit-distances-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove a power saving for the planar unit-distance problem: for some absolute $`\\beta\\lt 4/3`$, every set of n points in the Euclidean plane determines $`O(n^\\beta)`$ unordered pairs at unit distance.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A power saving for planar unit distances",
"titleZh": "平面单位距离问题的一个幂次节省",
"details": {
"overview": "该稿件研究欧几里得平面上的单位距离问题：给定n个点，能确定多少个无序点对恰相距1。作者声称证明了存在绝对常数β<4/3，使任意n点集的单位距离点对数不超过O(n^β)，即相对平凡上界取得幂次节省。若成立，这将推进组合几何中关于单位距离数量的经典问题。需注意该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"研究对象为平面n点集的单位距离无序点对数量。",
"作者声称存在绝对常数β<4/3，使单位距离点对数为O(n^β)。",
"结果形式为相对平凡上界的幂次节省，属组合几何问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"breakthrough": true,
"breakthroughField": "AI 与数学",
"interest": []
},
{
"id": "fec18b767a5a554c",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Nonuniqueness for the periodic hard-sphere Boltzmann equation",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove nonuniqueness for the periodic hard-sphere Boltzmann equation by constructing two distinct global renormalized solutions with the same nonnegative initial density on $`\\mathbb T^3\\times\\mathbb R^3`$. This density has bounded velocity support and finite mass, energy, and absolute entropy. Both solutions conserve local mass and total momentum and satisfy the global energy and entropy-dissipation inequalities. On a common initial interval, they are strongly continuous in L1, and their collision gains and losses are integrable.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Nonuniqueness for the periodic hard-sphere Boltzmann equation",
"titleZh": "周期硬球Boltzmann方程的非唯一性",
"details": {
"overview": "该稿件研究环面与速度空间上的周期硬球Boltzmann方程。作者声称构造了具有同一非负初始密度的两个不同全局重整化解，该初始密度速度支撑有界且质量、能量与绝对熵有限；两解均保持局部质量与总动量守恒，并满足全局能量与熵耗散不等式，在共同初始区间上L1强连续，碰撞增益与损失可积。若成立，表明该方程在给定初始数据下解不唯一。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"构造同一初始密度下的两个不同全局重整化解。",
"初始密度速度支撑有界，质量、能量与绝对熵有限。",
"两解满足局部质量与总动量守恒及能量、熵耗散不等式。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "fc989e234ed03881",
"section": "papers",
"category": "组合数学与图论",
"title": "Entropy and Face Dimension of the Perfect-Matching Polytope",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the perfect-matching entropy conjecture of Anari, Oveis Gharan, and Vinzant. For every feasible vector x of perfect-matching edge marginals in a loopless labelled multigraph on $`2m\\ge2`$ vertices, the maximum entropy $`H(x)`$ of a matching law with marginals x satisfies\n\n$`\\displaystyle F(x)-(2-2/m)B(x)\\le H(x)\\le F(x),`$\n\nwhere $`F(x)=-\\sum_e x_e\\log x_e`$ and $`B(x)=-\\sum_e(1-x_e)\\log(1-x_e)`$. This bound holds throughout the polytope, including its boundary. We also prove the sharp bound $`|\\mathop{\\mathrm{supp}}\\nolimits x|-\\dim F_x\\le3m-2`$, where Fx is the minimal face of the perfect-matching polytope containing x.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Entropy and Face Dimension of the Perfect-Matching Polytope",
"titleZh": "完美匹配多面体的熵与面维数",
"details": {
"overview": "该稿件研究无环标号多重图上完美匹配边边缘向量的熵。作者声称证明了Anari、Oveis Gharan与Vinzant提出的完美匹配熵猜想：对每个可行边缘向量x，匹配律最大熵H(x)满足F(x)−(2−2/m)B(x)≤H(x)≤F(x)，其中F与B分别为基于x_e和1−x_e的熵型量，且界在多面体边界也成立。稿件还声称证明了支撑集大小与含x最小面维数之差的尖锐上界3m−2。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"声称证明完美匹配熵猜想，给出H(x)的上下界。",
"界在整个完美匹配多面体上成立，包括边界。",
"另证支撑集大小与最小面维数之差的尖锐界3m−2。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "f86469048c727f83",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.11 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.11",
"date": "2026-09-23",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-23T04:50:17+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.11 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.11 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "f65281ac93d34cde",
"section": "papers",
"category": "组合数学与图论",
"title": "A translational tile with no fully periodic tiling in dimension three",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a finite translational tile in ℤ3 that admits tilings but no fully periodic tiling. Its unit-cube thickening has the same property in ℝ3, even when arbitrary real translations are allowed. This gives a negative resolution of the periodic tiling conjecture in dimension three.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A translational tile with no fully periodic tiling in dimension three",
"titleZh": "三维中一个无完全周期铺砌的平移铺砌块",
"details": {
"overview": "该稿件研究离散与连续空间中的平移铺砌。作者声称在ℤ³中构造了一个有限平移铺砌块，它允许铺砌但不存在完全周期铺砌；其单位立方体加厚在ℝ³中即使允许任意实平移也保持该性质。摘要表示这给出了三维周期铺砌猜想的否定解决。若成立，将说明高维中“可铺砌必可周期铺砌”的直觉不普遍成立。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"在ℤ³构造有限平移铺砌块，可铺砌但无完全周期铺砌。",
"单位立方体加厚在ℝ³中允许任意实平移仍具该性质。",
"作者声称由此否定解决三维周期铺砌猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "f6363c111571d39c",
"section": "news",
"category": "行业新闻",
"title": "ChatGPT Ads expands to Southeast Asia and Taiwan",
"summary": "该官方发布信息显示，ChatGPT Ads 将扩展至东南亚和台湾地区，使符合条件的企业能够在超过60个国家触达用户。",
"url": "https://openai.com/index/chatgpt-ads-expands-southeast-asia-taiwan",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T02:00:00+00:00",
"titleEn": "ChatGPT Ads expands to Southeast Asia and Taiwan",
"titleZh": "ChatGPT Ads 扩展至东南亚和台湾地区",
"details": {
"overview": "该官方发布信息显示，ChatGPT Ads 将扩展至东南亚和台湾地区，使符合条件的企业能够在超过60个国家触达用户。原文未说明具体上线日期、广告形式、定价、资格标准或各市场的开放节奏，也未给出效果数据。可确认的是，此次扩展延续了该广告产品的地域覆盖，并将东南亚与台湾地区纳入其中。相关推出范围和限制应以原文为准。",
"keyPoints": [
"ChatGPT Ads 扩展至东南亚和台湾地区。",
"符合条件的企业可在超过60个国家触达用户。",
"当前收录材料未提供上线时间、广告形式与定价细节。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "f60fd4ae4a12a208",
"section": "papers",
"category": "数学物理与量子信息",
"title": "Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For each fixed Kerr spacetime with mass M > 0 and rotation $`0\\lt \\mathfrak a\\lt M`$, we prove that a dense Gδ set of nearby smooth, complete two-ended vacuum data has a maximal globally hyperbolic development with no future C1 extension. The neighborhood and genericity are defined in a weighted smooth topology, and ambient extensions may be nonvacuum.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes",
"titleZh": "旋转次极端Kerr时空附近的通用C1未来不可延拓性",
"details": {
"overview": "该稿件研究固定Kerr时空（质量M>0、旋转0 0, resolving the all-temperature lattice mass-generation conjecture for this periodic state. Under the stated cutoff scaling, the mass bounds are uniform in independently fixed physical units. A continuum spectral interpretation requires separate convergence hypotheses for the transfer semigroup and the block observables.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Sharp mass bounds for the two-dimensional O(4) model",
"titleZh": "二维O(4)模型的尖锐质量界",
"details": {
"overview": "该稿件研究二维最近邻O(4)模型。作者声称对充分大的逆耦合β，完整转移间隙（含旋转不变局部可观测量扇区）被√β e^{−πβ}的正倍数上下夹住；并证明模型有唯一周期局部极限，且每个有限β>0处完整间隙为正，从而解决该周期态的全温度格点质量生成猜想。摘要还说明质量界在给定截断标度下对独立固定的物理单位一致，连续谱解释需额外收敛假设。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"声称大β时完整转移间隙由√β e^{−πβ}的正倍数上下界控制。",
"证明唯一周期局部极限及每个有限β>0处完整间隙为正。",
"作者称由此解决该周期态的全温度格点质量生成猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "ee52c90635d12190",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Expected amenable subalgebras preserving core commutants",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every inclusion $`N\\subset M`$ of von Neumann algebras with separable preduals and a faithful normal conditional expectation contains an expected amenable subalgebra $`P\\subset N`$ such that $`P'\\cap c(M)=N'\\cap c(M)`$, where $`c(M)`$ denotes the continuous core of M. This resolves the relative bicentralizer conjecture in this setting.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Expected amenable subalgebras preserving core commutants",
"titleZh": "保持核心交换子的期望顺从子代数",
"details": {
"overview": "该稿件研究具有可分预对偶与忠实正规条件期望的von Neumann代数包含N⊂M。作者声称存在期望顺从子代数P⊂N，使得P′∩c(M)=N′∩c(M)，其中c(M)为M的连续核心，并称由此在该设定下解决相对双中心化子猜想。若成立，这将在算子代数中把顺从子代数的存在性与核心交换子保持联系起来。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"设定为可分预对偶、带忠实正规条件期望的包含N⊂M。",
"声称存在期望顺从子代数P⊂N保持连续核心交换子。",
"作者称由此解决该设定下的相对双中心化子猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "ee4792edda679073",
"section": "papers",
"category": "分析与偏微分方程",
"title": "The arithmetic category and stable recovery of lattice factors",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove stable canonical recovery for scalar-twisted group factors of ICC groups commensurable with property-$`(T)`$ lattices over characteristic-zero local fields. Every specified stable isomorphism to a scalar-twisted factor of any countably infinite ICC group recovers the group, the cocycle up to a normalized cochain, and equal amplification scales, with an implementing partial isometry in the given matrix corners. We compute the arithmetic correspondence subcategory for arbitrary countable ICC groups, including all bounded maps, summands, conjugates, and Connes fusion, and combine it with the companion's arithmetic exhaustion theorem. Multiplication also recovers arbitrary finite-index factor neighbors, with the exact projective condition on the matched cocycle ratio.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The arithmetic category and stable recovery of lattice factors",
"titleZh": "算术范畴与格因子的稳定恢复",
"details": {
"overview": "该稿件研究ICC群标量扭曲群因子的稳定恢复。作者声称对与特征零局部域上性质(T)格可公度的ICC群，其标量扭曲群因子具有稳定典范恢复：每个到任意可数无限ICC群标量扭曲因子的指定稳定同构可恢复群、模正规上链的余圈及相同放大尺度，并在给定矩阵角中给出实现部分等距。稿件还计算任意可数ICC群的算术对应子范畴，并结合伴随的算术穷尽定理；乘法还恢复有限指数因子邻域及匹配余圈比的投影条件。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"对象为与性质(T)格可公度的ICC群的标量扭曲群因子。",
"声称稳定同构可恢复群、余圈模正规上链及放大尺度。",
"计算任意可数ICC群的算术对应子范畴并处理有限指数邻域。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数论与算术几何",
"interest": []
},
{
"id": "edea1e0f6e7eb80e",
"section": "papers",
"category": "组合数学与图论",
"title": "A classification of finite Euclidean Ramsey configurations",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-classification-of-finite-Euclidean-Ramsey-configurations-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We classify finite Euclidean Ramsey configurations by a necessary and sufficient tensor condition over their coordinate fields. The Ramsey property here concerns monochromatic congruent copies at the original scale under arbitrary finite colorings. The criterion shows that every nonempty subtransitive set and every nonempty set of at most five points on a circle is Ramsey. In particular, some Ramsey cyclic quadrilaterals are not subtransitive, disproving the necessity direction of the Leader–Russell–Walters conjectured characterization.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A classification of finite Euclidean Ramsey configurations",
"titleZh": "有限欧氏Ramsey构型的分类",
"details": {
"overview": "稿件研究有限欧氏Ramsey构型的分类问题，作者声称给出一个关于坐标域的充要张量条件。这里的Ramsey性质指在任意有限染色下，原尺度上存在单色全等副本。摘要表示该判据可推出每个非空次传递集以及圆上至多五点的非空集都是Ramsey的；并称存在非次传递的Ramsey循环四边形，从而否定Leader–Russell–Walters猜想刻画中的必要性方向。该结果若成立，将修正对欧氏Ramsey构型的既有刻画。",
"keyPoints": [
"提出关于坐标域的充要张量条件，用于分类有限欧氏Ramsey构型。",
"作者声称圆上至多五点的非空集与每个非空次传递集均为Ramsey。",
"构造非次传递的Ramsey循环四边形，否定原猜想必要性方向。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "ebfecae1d27d382b",
"section": "papers",
"category": "组合数学与图论",
"title": "The crossing number of complete bipartite graphs",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-crossing-number-of-complete-bipartite-graphs-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Zarankiewicz crossing-number conjecture, resolving Turán's brickyard problem. For all positive integers m, n, the ordinary crossing number of the complete bipartite graph $`K_{m,n}`$ is\n\n$`\\displaystyle \\left\\lfloor\\frac m2\\right\\rfloor \\left\\lfloor\\frac{m-1}{2}\\right\\rfloor \\left\\lfloor\\frac n2\\right\\rfloor \\left\\lfloor\\frac{n-1}{2}\\right\\rfloor.`$",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The crossing number of complete bipartite graphs",
"titleZh": "完全二部图的交叉数",
"details": {
"overview": "稿件研究完全二部图K_{m,n}的普通交叉数，作者声称证明了Zarankiewicz交叉数猜想，并由此解决Turán的砖厂问题。摘要给出的公式为⌊m/2⌋⌊(m−1)/2⌋⌊n/2⌋⌊(n−1)/2⌋，对所有正整数m、n成立。该问题长期是拓扑图论中的核心猜想之一；若证明成立，将统一确定完全二部图的交叉数。需注意这是AI产生的手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"作者声称证明Zarankiewicz交叉数猜想，解决Turán砖厂问题。",
"给出K_{m,n}交叉数的闭式公式，声称对所有正整数m、n成立。",
"结果属拓扑图论中长期未决的核心猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "ebca3a8ae6f43950",
"section": "papers",
"category": "几何与拓扑",
"title": "Positively curved Einstein four-manifolds",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Positively-curved-Einstein-four-manifolds-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the classification conjecture for connected smooth closed Einstein four-manifolds with strictly positive sectional curvature. Up to positive scaling and isometry, every such manifold is the round four-sphere, the complex projective plane with its Fubini–Study metric, or real projective four-space with its round metric. No orientability assumption is needed.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Positively curved Einstein four-manifolds",
"titleZh": "正曲率爱因斯坦四维流形",
"details": {
"overview": "稿件研究连通、光滑、闭的爱因斯坦四维流形，且截面曲率严格为正。作者声称证明了此类流形的分类猜想：在正缩放与等距意义下，每个这样的流形只能是标准四维球面、带Fubini–Study度量的复射影平面，或带圆度量的实射影四维空间，且无需可定向性假设。摘要表示该分类不依赖定向条件。该结论若成立，将完成正曲率爱因斯坦四维流形的分类。",
"keyPoints": [
"研究对象为截面曲率严格为正的连通闭光滑爱因斯坦四维流形。",
"作者声称分类仅有球面、复射影平面与实射影四维空间三类。",
"摘要强调分类无需可定向性假设，且允许正缩放与等距。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "e8fafdbd39b55471",
"section": "papers",
"category": "代数几何",
"title": "Positivity of Serre's Intersection Multiplicity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Serre's positivity conjecture, including ramified mixed characteristic. If two nonzero finitely generated modules over a regular local ring have tensor product of finite length and complementary dimensions, then their intersection multiplicity is strictly positive.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Positivity of Serre's Intersection Multiplicity",
"titleZh": "Serre相交重数的正性",
"details": {
"overview": "稿件研究正则局部环上两个非零有限生成模的相交重数正性问题。作者声称证明了Serre正性猜想，包括分歧混合特征情形。摘要给出的条件是：若两模的张量积具有有限长度且维数互补，则其相交重数严格为正。该猜想是交换代数与代数几何交叉中的重要问题；若证明成立，将把正性结论推广到此前未覆盖的分歧混合特征情形。需注意这是AI产生的手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"作者声称证明Serre正性猜想，覆盖分歧混合特征情形。",
"条件为两模张量积有限长且维数互补，结论为相交重数严格正。",
"问题位于交换代数与代数几何交叉处。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数论与算术几何",
"interest": []
},
{
"id": "e275a6af0c6637b7",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Cuntz comparison and Jiang–Su absorption",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that strict comparison in the extended-functional sense implies Jiang–Su absorption for separable simple nuclear non-elementary C∗-algebras. This resolves the corresponding implication of the Toms–Winter regularity problem, including nonunital algebras and allowing unbounded traces. More generally, every separable nuclear C∗-algebra whose Cuntz semigroup is almost unperforated and fully almost divisible absorbs the Jiang–Su algebra.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Cuntz comparison and Jiang–Su absorption",
"titleZh": "Cuntz比较与Jiang–Su吸收",
"details": {
"overview": "稿件研究可分、单、核、非初等C∗-代数中的正则性问题。作者声称证明：扩展泛函意义下的严格比较蕴含Jiang–Su吸收，从而解决Toms–Winter正则性问题中相应的蕴含方向，并覆盖非单位代数、允许无界迹。摘要还表示，更一般地，凡Cuntz半群几乎不可穿孔且完全几乎可除的可分核C∗-代数都吸收Jiang–Su代数。该结果若成立，将推进C∗-代数分类纲领中的正则性判据。",
"keyPoints": [
"作者声称扩展泛函意义下的严格比较蕴含Jiang–Su吸收。",
"结果覆盖非单位C∗-代数，并允许无界迹。",
"更一般地，Cuntz半群几乎不可穿孔且完全几乎可除时吸收Jiang–Su代数。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "e15207a1bb4bbfd7",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.158.0-alpha.2 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.158.0-alpha.2",
"date": "2026-09-23",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-23T13:07:10+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.158.0-alpha.2 测试版发布",
"details": {
"overview": "Codex CLI 0.158.0-alpha.2 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "e0aec99487d3d38d",
"section": "papers",
"category": "概率与统计",
"title": "A directional zero–one law under strict ellipticity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the directional zero–one conjecture for nearest-neighbor random walks in independent and identically distributed strictly elliptic environments on ℤd, d ≥ 3: the probability of escape in each fixed nonzero real direction is zero or one. Only strict positivity of the transition probabilities is required; no uniform lower bound or moment assumption is imposed.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A directional zero–one law under strict ellipticity",
"titleZh": "严格椭圆性下的方向零一律",
"details": {
"overview": "稿件研究ℤd（d≥3）上独立同分布严格椭圆环境中的最近邻随机游走。作者声称证明了方向零一猜想：沿每个固定非零实方向的逃逸概率只能为0或1。摘要强调，证明只要求转移概率严格为正，不需要一致下界，也不需要矩假设。该问题属于随机环境中的随机游走与方向性极限行为研究；若成立，将在很弱的椭圆性条件下确立方向零一律。",
"keyPoints": [
"研究对象为ℤd（d≥3）上独立同分布严格椭圆环境中的最近邻随机游走。",
"作者声称每个固定非零实方向的逃逸概率为0或1。",
"证明仅需转移概率严格为正，无需一致下界或矩假设。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论",
"interest": []
},
{
"id": "e0a43c602f8363de",
"section": "news",
"category": "行业新闻",
"title": "Grab and OpenAI bring practical AI skills to Southeast Asia",
"summary": "该官方发布信息称，OpenAI 与 Grab 推出区域性项目“GO Forward with AI”，旨在帮助东南亚地区3万名合作伙伴建立实用 AI 技能。",
"url": "https://openai.com/index/grab-openai-ai-skills-southeast-asia",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T00:00:00+00:00",
"titleEn": "Grab and OpenAI bring practical AI skills to Southeast Asia",
"titleZh": "Grab 与 OpenAI 为东南亚带来实用 AI 技能",
"details": {
"overview": "该官方发布信息称，OpenAI 与 Grab 推出区域性项目“GO Forward with AI”，旨在帮助东南亚地区3万名合作伙伴建立实用 AI 技能。原文未说明项目课程内容、培训形式、时间安排、覆盖国家或参与条件，也未提供效果评估。可确认的是，双方将合作对象定位为合作伙伴群体，并以提升实际应用能力为目标。具体推出范围和限制应以原文为准。",
"keyPoints": [
"OpenAI 与 Grab 推出区域项目 GO Forward with AI。",
"项目目标是帮助东南亚3万名合作伙伴建立实用 AI 技能。",
"当前收录材料未提供课程形式、时间表与覆盖国家细节。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "df001abad8ef6c9d",
"section": "papers",
"category": "代数几何",
"title": "The strong hyperkähler SYZ conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the strong hyperkähler SYZ conjecture: every holomorphic line bundle with nonzero nef isotropic first Chern class on a compact irreducible holomorphic symplectic Kähler manifold is semiample.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The strong hyperkähler SYZ conjecture",
"titleZh": "强hyperkähler SYZ猜想",
"details": {
"overview": "稿件研究紧致不可约全纯辛Kähler流形上的全纯线束。作者声称证明了强hyperkähler SYZ猜想：若全纯线束的第一陈类非零、nef且迷向，则该线束半丰沛。摘要只给出这一核心陈述，未展开证明细节或附加条件。该猜想联系hyperkähler几何中的Lagrange纤维化与丰沛性理论；若成立，将为相关线束的半丰沛性提供统一判据。需注意这是AI产生的手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"研究对象为紧致不可约全纯辛Kähler流形上的全纯线束。",
"作者声称第一陈类非零、nef且迷向的线束必半丰沛。",
"该陈述即强hyperkähler SYZ猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "dd46e468e2b84d05",
"section": "news",
"category": "模型动态",
"title": "Introducing GPT-6 Sol and Luna",
"summary": "该官方发布信息介绍 GPT-6 Sol 和 Luna 两款模型，称二者将前沿智能带入日常工作，并在能力与成本之间提供不同平衡。",
"url": "https://openai.com/index/introducing-gpt-6-sol-and-luna",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-22T18:00:00+00:00",
"titleEn": "Introducing GPT-6 Sol and Luna",
"titleZh": "推出 GPT-6 Sol 与 Luna",
"details": {
"overview": "该官方发布信息介绍 GPT-6 Sol 和 Luna 两款模型，称二者将前沿智能带入日常工作，并在能力与成本之间提供不同平衡。原文未说明两款模型的具体参数、上下文长度、可用平台、定价、上线地区或基准测试结果，也未解释 Sol 与 Luna 各自的定位差异。可确认的是，发布方将两者描述为面向日常工作的前沿模型，并以能力与成本的不同组合作为区分点。相关范围与限制应以原文为准。",
"keyPoints": [
"发布 GPT-6 Sol 与 Luna 两款模型。",
"官方称两者面向日常工作并带来前沿智能。",
"两款模型在能力与成本之间提供不同平衡。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "dc57c759b35eca7a",
"section": "papers",
"category": "动力系统与遍历论",
"title": "A smooth three-torus diffeomorphism with simple Lebesgue spectrum",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We solve the probability-preserving form of Banach's simple Lebesgue-spectrum problem in smooth dynamics. We construct a C∞ diffeomorphism of the three-torus that preserves standard volume and whose Koopman operator has simple Lebesgue spectrum on the entire mean-zero L2 space.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A smooth three-torus diffeomorphism with simple Lebesgue spectrum",
"titleZh": "具有简单Lebesgue谱的光滑三维环面微分同胚",
"details": {
"overview": "稿件研究保测动力系统中的Banach简单Lebesgue谱问题。作者声称在光滑动力系统范围内解决了该问题的保概率形式：构造出三维环面上的C∞微分同胚，它保持标准体积，且其Koopman算子在全体均值为零的L2空间上具有简单Lebesgue谱。当前收录摘要未给出构造细节或谱论证步骤。该结果若成立，将为光滑系统中长期开放的简单Lebesgue谱问题提供首个三维环面例子。",
"keyPoints": [
"作者声称解决Banach简单Lebesgue谱问题的保概率形式。",
"构造三维环面C∞微分同胚，保持标准体积。",
"其Koopman算子在均值为零的L2空间上具有简单Lebesgue谱。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "da96cfbd257ce570",
"section": "papers",
"category": "代数与表示论",
"title": "Parabolic intersections in Artin groups",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every intersection of parabolic subgroups of any finite-rank Artin group, with arbitrary finite or infinite Coxeter labels, is parabolic. This resolves the Parabolic Intersection Conjecture affirmatively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Parabolic intersections in Artin groups",
"titleZh": "Artin群中的抛物交",
"details": {
"overview": "稿件研究任意有限秩Artin群的抛物子群交。作者声称证明了：任意有限秩Artin群（Coxeter标号可有限或无限）中，任意多个抛物子群的交仍是抛物子群，从而肯定解决抛物交猜想。当前收录摘要未给出证明方法或对无限标号情形的额外限制。该问题属于Artin群与Coxeter群结构理论；若成立，将统一处理有限与无限Coxeter标号下的抛物交封闭性。",
"keyPoints": [
"研究对象为任意有限秩Artin群的抛物子群交。",
"作者声称任意多个抛物子群的交仍为抛物子群。",
"结果覆盖有限与无限Coxeter标号，肯定解决抛物交猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "d9c3aa123fb5e105",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Kadison's similarity theorem through uniform derivation estimates",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every bounded complex-linear unital algebra homomorphism from a unital complex C∗-algebra into the bounded operators on an arbitrary Hilbert space is similar to a $`*`$-homomorphism. This resolves Kadison's similarity conjecture positively. We also obtain one universal hyperreflexivity constant for all unital von Neumann algebras on arbitrary complex Hilbert spaces.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Kadison's similarity theorem through uniform derivation estimates",
"titleZh": "通过一致导子估计证明Kadison相似定理",
"details": {
"overview": "稿件研究C∗-代数到任意Hilbert空间上有界算子的有界复线性单位代数同态。作者声称证明每个这样的同态都相似于一个∗-同态，从而肯定解决Kadison相似猜想。摘要还表示，对所有任意复Hilbert空间上的单位von Neumann代数，得到一个统一的超自反常数。该结果若成立，将把Kadison相似性问题与一致导子估计、超自反性联系起来。需注意这是AI产生的手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"作者声称C∗-代数到有界算子的单位代数同态均相似于∗-同态。",
"由此肯定解决Kadison相似猜想。",
"另对所有单位von Neumann代数得到统一超自反常数。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "d7bddc5289fb45fd",
"section": "papers",
"category": "分析与偏微分方程",
"title": "A torsion-free counterexample to reduced Baum–Connes injectivity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove rational injectivity of the coefficient-free reduced Baum–Connes assembly map for torsion-free groups. Specifically, we construct a finitely generated torsion-free discrete group whose degree-zero assembly map has a kernel class of infinite order.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A torsion-free counterexample to reduced Baum–Connes injectivity",
"titleZh": "无挠群上约化Baum–Connes单射性的反例",
"details": {
"overview": "稿件研究无系数约化Baum–Connes装配映射的有理单射性。作者声称给出反例：构造一个有限生成、无挠的离散群，其零次装配映射的核中含有一个无限阶类，从而否定无挠群情形下的有理单射性。摘要未说明群的其余性质或构造方法。该结果若成立，将推翻此前对无挠群上约化Baum–Connes单射性的普遍预期。需注意这是AI产生的手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"作者声称否定无挠群上无系数约化Baum–Connes装配映射的有理单射性。",
"构造有限生成无挠离散群，其零次装配映射核含无限阶类。",
"反例针对有理单射性，而非整数单射性。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "d737f348b305bed4",
"section": "papers",
"category": "代数与表示论",
"title": "The Deligne-Drinfeld conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Deligne-Drinfeld-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Deligne–Drinfeld conjecture: the rational Grothendieck–Teichmüller Lie algebra is freely generated by one element in every odd weight at least three, with the corresponding isomorphism after weight completion.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Deligne-Drinfeld conjecture",
"titleZh": "Deligne–Drinfeld猜想",
"details": {
"overview": "稿件研究Grothendieck–Teichmüller李代数的结构。作者声称证明了Deligne–Drinfeld猜想：有理Grothendieck–Teichmüller李代数由每个至少为3的奇数权中各一个元素自由生成，并在权完备化后给出相应同构。摘要未展开生成元的具体构造或完备化细节。该猜想刻画了Grothendieck–Teichmüller群及其李代数的自由结构；若成立，将为该李代数提供完整的自由生成描述。",
"keyPoints": [
"作者声称证明Deligne–Drinfeld猜想。",
"有理Grothendieck–Teichmüller李代数由每个至少3的奇数权各一元素自由生成。",
"权完备化后给出相应同构。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "d6dc2036198efff2",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Vanishing of higher bounded Hochschild cohomology",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with values in the algebra itself, has a bounded primitive. Together with the established degree-one inner-derivation theorem, this resolves the Kadison–Ringrose cohomology conjecture positively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Vanishing of higher bounded Hochschild cohomology",
"titleZh": "高阶有界Hochschild上同调的消没",
"details": {
"overview": "稿件研究复von Neumann代数上取值于自身的有界Hochschild上同调。作者声称证明了次数至少为2的每个有界Hochschild余循环都有有界原语，并结合已有的次数1内导子定理，正面解决了Kadison–Ringrose上同调猜想。该结果若成立，将统一处理高阶上同调的消没问题，对算子代数上同调理论有重要意义。当前收录摘要未给出证明细节或独立验证信息。",
"keyPoints": [
"证明复von Neumann代数上次数≥2的有界Hochschild余循环均有有界原语。",
"结合次数1内导子定理，声称正面解决Kadison–Ringrose上同调猜想。",
"研究对象为取值于代数自身的有界Hochschild上同调。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "d5266dd35bd139f5",
"section": "papers",
"category": "其他数学",
"title": "Sharp integral fillings in CAT(0) spaces",
"summary": "OpenAI 数学相关研究材料。具体研究对象、结果及核验状态请查看详情。",
"url": "https://github.com/openai/math/blob/main/preprints/Sharp-integral-fillings-in-CAT(0)-spaces-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"source": "OpenAI 数学仓库",
"titleEn": "Sharp integral fillings in CAT(0) spaces",
"abstractEnglish": "Every compactly supported integral n -cycle, n ≥ 2, in a proper CAT(0) space bounds a compactly supported integral current with the sharp Euclidean mass bound. The theorem allows arbitrary integer multiplicities and unrestricted ambient dimension. In particular, we prove the Euclidean Cartan–Hadamard isoperimetric conjecture in dimensions at least three.",
"titleZh": "CAT(0) 空间中的尖锐积分填充",
"details": {
"overview": "该研究手稿摘要声称，在真 CAT(0) 空间中，每个紧支撑整 n-链（n ≥ 2）都界定一个紧支撑整电流，并满足尖锐的欧几里得质量界；定理允许任意整数重数和不受限的环境维数。摘要还称，由此证明了至少三维情形下的欧几里得 Cartan–Hadamard 等周猜想。该稿件为 AI 产生的研究手稿，收录不表示已完成独立审查或同行评议，上述结论应视为作者声称，尚待数学界检验。",
"keyPoints": [
"稿件声称真 CAT(0) 空间中紧支撑整 n-链具有尖锐欧几里得质量界填充。",
"定理允许任意整数重数与不受限环境维数。",
"摘要称由此证明至少三维的欧几里得 Cartan–Hadamard 等周猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "d4b6a8da63359750",
"section": "papers",
"category": "概率与统计",
"title": "Cardy’s formula for critical Poisson–Voronoi percolation",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Cardys-formula-for-critical-Poisson-Voronoi-percolation-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Cardy's formula for annealed crossing probabilities in critical planar Poisson–Voronoi percolation in every bounded Jordan quadrilateral. This proves the annealed crossing-probability form of the conformal-invariance conjecture for this model.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Cardy’s formula for critical Poisson–Voronoi percolation",
"titleZh": "临界Poisson–Voronoi渗流的Cardy公式",
"details": {
"overview": "稿件研究临界平面Poisson–Voronoi渗流在任意有界Jordan四边形中的退火穿越概率。作者声称证明了Cardy公式，从而验证了该模型共形不变性猜想的退火穿越概率形式。该结果将Cardy公式从其他平面渗流模型推广到Poisson–Voronoi模型，对理解临界渗流的共形不变性有重要意义。摘要未提供证明方法或独立审查信息。",
"keyPoints": [
"证明临界平面Poisson–Voronoi渗流在任意有界Jordan四边形中的Cardy公式。",
"结果针对退火穿越概率，验证共形不变性猜想的相应形式。",
"研究对象为临界Poisson–Voronoi渗流模型。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论",
"interest": []
},
{
"id": "d2634392c9c92732",
"section": "papers",
"category": "代数几何",
"title": "Nagata's conjecture for plane curves",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that a nonzero effective plane curve of degree d at r ≥ 10 very general complex points has total multiplicity strictly less than $`d\\sqrt r`$. The inequality holds simultaneously for all curves, including reducible and nonreduced curves, and establishes Nagata's conjecture in its strict, nonhomogeneous form.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Nagata's conjecture for plane curves",
"titleZh": "平面曲线的Nagata猜想",
"details": {
"overview": "稿件研究平面代数曲线的Nagata猜想。作者声称证明了：对于r≥10个非常一般的复点，次数为d的非零有效平面曲线（包括可约与非约化曲线）的总重数严格小于d√r，从而建立了Nagata猜想的严格非齐次形式。该结果若成立，将解决代数几何中关于平面曲线重数下界的长期猜想。当前收录摘要未给出证明细节或独立验证。",
"keyPoints": [
"证明r≥10个非常一般复点上次数d的非零有效平面曲线总重数 0 on a fixed smooth closed connected Riemannian surface has nodal length at most $`C\\sqrt\\lambda`$. Together with the known lower bound, this proves Yau's conjecture in this setting.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Sharp nodal length on smooth surfaces",
"titleZh": "光滑曲面上尖锐的节点长度",
"details": {
"overview": "稿件研究固定光滑闭连通黎曼曲面上非零实拉普拉斯特征函数的节点集长度。作者声称证明特征值λ>0时节点长度至多C√λ，并结合已知下界，在该设定下证明Yau猜想。若成立，这将给出节点长度关于特征值的尖锐上界，对谱几何与节点集研究有基础意义。需注意该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"研究对象为光滑闭连通黎曼曲面上拉普拉斯特征函数的节点长度",
"作者声称节点长度上界为C√λ",
"结合已知下界，声称在该设定下证明Yau猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "b877773c9b8e3f32",
"section": "papers",
"category": "代数与表示论",
"title": "The Artinian Lex-Plus-Powers Betti Theorem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. For every homogeneous ideal containing such a sequence, the corresponding lex-plus-powers ideal has the same Hilbert function and at least as large a graded Betti number in every homological and internal degree.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Artinian Lex-Plus-Powers Betti Theorem",
"titleZh": "Artinian字典加幂Betti定理",
"details": {
"overview": "稿件研究齐次正则序列与字典加幂理想的分次Betti数。作者声称在任意特征零域上，对任意正长度、次数至少二的齐次正则序列证明Eisenbud–Green–Harris与字典加幂猜想：对包含该序列的每个齐次理想，对应字典加幂理想具有相同Hilbert函数，且在每个同调与内次数上分次Betti数不小于原理想。若成立，将推进交换代数中关于Betti数上界的经典问题。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"研究对象为特征零域上齐次正则序列与字典加幂理想",
"作者声称证明Eisenbud–Green–Harris与字典加幂猜想",
"对应字典加幂理想Hilbert函数相同且各分次Betti数不小于原理想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "b5dd1f85b7002cef",
"section": "papers",
"category": "理论计算机科学",
"title": "Constant-factor hardness of directed feedback vertex set",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Constant-factor-hardness-of-directed-feedback-vertex-set-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Approximating minimum directed feedback vertex set within any fixed constant factor is NP-hard, even on unweighted digraphs.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Constant-factor hardness of directed feedback vertex set",
"titleZh": "有向反馈顶点集的常数因子硬度",
"details": {
"overview": "稿件研究最小有向反馈顶点集问题的近似硬度。作者声称证明：即使限制在无权有向图上，在任意固定常数因子内近似该问题都是NP难的。该结论若成立，将说明有向反馈顶点集不存在常数因子近似算法（除非P=NP），对图论近似算法与硬度研究有重要意义。需注意该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"研究对象为无权有向图上的最小有向反馈顶点集",
"作者声称任意固定常数因子近似均NP难",
"结果意味着不存在常数因子近似算法，除非P=NP"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "b5aecb828f2db722",
"section": "papers",
"category": "代数与表示论",
"title": "An infinite finitely presented periodic group",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-infinite-finitely-presented-periodic-group-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct an infinite group with an ordinary finite presentation in which every element has finite order, answering the finitely presented Burnside question negatively. We also construct an infinite-dimensional finitely presented nonunital nil associative algebra over 𝔽2 that is Jacobson radical but not nilpotent. Its unitization is finitely presented, algebraic, and infinite-dimensional. These algebras answer the finitely presented nil- and radical-algebra nilpotence questions and the finite-presentation version of Kurosh's algebraic finiteness question negatively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An infinite finitely presented periodic group",
"titleZh": "一个无限有限呈现周期群",
"details": {
"overview": "稿件研究有限呈现Burnside问题及相关代数结构。作者声称构造一个具有普通有限呈现且每个元素阶有限的无限群，从而否定有限呈现Burnside问题；还构造𝔽2上无限维有限呈现非单位零结合代数，为Jacobson根但非幂零，其单位化有限呈现、代数且无限维。摘要称这些代数否定有限呈现零代数与根代数幂零问题及Kurosh代数有限性问题的有限呈现版本。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"构造无限、有限呈现且每元素有限阶的群，否定有限呈现Burnside问题",
"构造𝔽2上无限维有限呈现非单位零结合代数，Jacobson根但非幂零",
"作者声称这些结果否定若干有限呈现版本的代数幂零与有限性问题"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "b5320509f9d75313",
"section": "papers",
"category": "组合数学与图论",
"title": "The hypercube Ramsey number has linear order",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-hypercube-Ramsey-number-has-linear-order-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the two-color Ramsey number of the n-dimensional binary cube is at most $`C2^n`$, where C is an absolute constant. This resolves positively the hypercube Ramsey conjecture of Burr and Erdős.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The hypercube Ramsey number has linear order",
"titleZh": "超立方体Ramsey数具有线性阶",
"details": {
"overview": "稿件研究n维二元超立方体的双色Ramsey数。作者声称证明该Ramsey数至多C2^n，其中C为绝对常数，从而正面解决Burr与Erdős提出的超立方体Ramsey猜想。若成立，这将把超立方体Ramsey数从已知的指数上界改进为线性阶，对Ramsey理论与超立方体组合结构有重要意义。需注意该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"研究对象为n维二元超立方体的双色Ramsey数",
"作者声称其上界为C2^n，C为绝对常数",
"声称正面解决Burr与Erdős的超立方体Ramsey猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "b5151f21489a7d95",
"section": "papers",
"category": "组合数学与图论",
"title": "The crossing number of complete graphs",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-crossing-number-of-complete-graphs-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Harary–Hill conjecture: for every positive integer n, the ordinary crossing number of the complete graph Kn is\n\n$`\\displaystyle \\frac14\\left\\lfloor\\frac n2\\right\\rfloor \\left\\lfloor\\frac{n-1}{2}\\right\\rfloor \\left\\lfloor\\frac{n-2}{2}\\right\\rfloor \\left\\lfloor\\frac{n-3}{2}\\right\\rfloor.`$",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The crossing number of complete graphs",
"titleZh": "完全图的交叉数",
"details": {
"overview": "该稿件声称证明了Harary–Hill猜想：对每个正整数n，完全图Kn的普通交叉数等于四分之一乘以⌊n/2⌋、⌊(n-1)/2⌋、⌊(n-2)/2⌋、⌊(n-3)/2⌋的连乘积。摘要仅给出这一公式，未说明证明方法或验证细节。若成立，将为图论中完全图交叉数这一长期问题给出统一闭式答案。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称证明Harary–Hill猜想，给出完全图Kn交叉数的闭式公式。",
"公式为⌊n/2⌋⌊(n-1)/2⌋⌊(n-2)/2⌋⌊(n-3)/2⌋的四分之一。",
"摘要未提供证明思路或独立验证信息。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "图论与组合数学",
"interest": []
},
{
"id": "b392a775c25c3c4d",
"section": "papers",
"category": "组合数学与图论",
"title": "Quasipolynomial Bounds for Arithmetic Progressions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Quasipolynomial-Bounds-for-Arithmetic-Progressions-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Erdős's conjecture that every set of positive integers with divergent reciprocal sum contains arithmetic progressions of every finite length. More quantitatively, for every fixed k ≥ 3, we show\n\n$`\\displaystyle r_k(N)\\le C_kN\\exp\\bigl(-c_k(\\log N)^{\\varepsilon_k}\\bigr)`$\n\nwith $`C_k,c_k,\\varepsilon_k\\gt 0`$, where $`r_k(N)`$ is the largest size of a subset of $`\\{1,\\ldots,N\\}`$ with no nonconstant k-term arithmetic progression.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Quasipolynomial Bounds for Arithmetic Progressions",
"titleZh": "算术级数的拟多项式界",
"details": {
"overview": "该稿件声称证明了Erdős猜想：倒数之和发散的任意正整数集合都包含任意有限长度的算术级数。摘要进一步给出定量估计：对每个固定k≥3，无k项算术级数的{1,…,N}子集最大规模rk(N)不超过CkN·exp(−ck(log N)^{εk})，其中Ck、ck、εk为正。摘要未说明证明技术。若成立，将同时推进组合数论中关于算术级数的经典问题。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称证明Erdős猜想：倒数和发散的正整数集含任意有限长算术级数。",
"给出rk(N)的上界CkN·exp(−ck(log N)^{εk})，k≥3固定。",
"摘要未交代证明方法，结论尚待独立审查。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数论",
"interest": []
},
{
"id": "b38ea80a6222ba52",
"section": "papers",
"category": "几何与拓扑",
"title": "A finite Smith–Toda complex V(4) at the prime 1009",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a Smith–Toda complex $`V(4)`$ at the prime 1009. It is an ordinary finite 1009-local spectrum whose Brown–Peterson homology is $`BP_*/(1009,v_1,v_2,v_3,v_4)`$, with its canonical comodule structure and generator in degree zero.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A finite Smith–Toda complex V(4) at the prime 1009",
"titleZh": "素数1009处的有限Smith–Toda复形V(4)",
"details": {
"overview": "该稿件声称在素数1009处构造了一个Smith–Toda复形V(4)。摘要说明它是一个普通的有限1009局部谱，其Brown–Peterson同调为BP*/(1009,v1,v2,v3,v4)，带有标准余模结构且生成元位于零次。当前收录摘要未给出构造细节或验证过程。若成立，将为稳定同伦论中Smith–Toda复形在较大素数处的存在性提供实例。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称在素数1009处构造有限1009局部谱V(4)。",
"其Brown–Peterson同调为BP*/(1009,v1,v2,v3,v4)，生成元在零次。",
"摘要未提供构造方法或独立验证。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数拓扑",
"interest": []
},
{
"id": "b31d6a65b01617a9",
"section": "news",
"category": "模型动态",
"title": "Better prompt caching for GPT-6",
"summary": "官方发布摘要表示，GPT-6 改进了提示缓存，具体包括更高的缓存命中率、新的诊断能力、显式断点以及若干控制项，目标是降低延迟和成本。",
"url": "https://openai.com/index/better-prompt-caching-for-gpt-6",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-22T21:00:00+00:00",
"titleEn": "Better prompt caching for GPT-6",
"titleZh": "GPT-6 的提示缓存改进",
"details": {
"overview": "官方发布摘要表示，GPT-6 改进了提示缓存，具体包括更高的缓存命中率、新的诊断能力、显式断点以及若干控制项，目标是降低延迟和成本。当前收录摘要未给出命中率提升幅度、延迟或成本的具体数值，也未说明这些改进的独立验证情况，相关效果应以官方后续技术说明为准。",
"keyPoints": [
"摘要称 GPT-6 提示缓存命中率提高，并新增诊断能力。",
"引入显式断点和控制项，官方称用于降低延迟与成本。",
"摘要未披露具体性能数字或独立验证结果。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "b16fa58aaf55a647",
"section": "papers",
"category": "组合数学与图论",
"title": "A counterexample to Hadwiger's conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Hadwigers-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove Hadwiger's conjecture by constructing arbitrarily large graphs whose chromatic number exceeds their Hadwiger number. The examples have independence number at most two, and even their ordinary fractional chromatic number exceeds their Hadwiger number. Thus they also disprove the fractional-coloring weakening discussed by Reed and Seymour.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A counterexample to Hadwiger's conjecture",
"titleZh": "Hadwiger猜想的一个反例",
"details": {
"overview": "该稿件声称否证了Hadwiger猜想：构造出任意大的图，使其色数超过Hadwiger数。摘要称这些例子的独立数至多为二，甚至其普通分数色数也超过Hadwiger数，因而也否证了Reed与Seymour讨论的分数着色弱化版本。当前收录摘要未给出构造细节或规模估计。若成立，将对图着色与图子式理论中的核心猜想产生重大影响。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称构造任意大图，使色数超过Hadwiger数，从而否证Hadwiger猜想。",
"例子独立数至多为二，分数色数也超过Hadwiger数。",
"同时声称否证Reed–Seymour讨论的分数着色弱化版本。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "图论与组合数学",
"breakthrough": true,
"breakthroughField": "AI 与数学",
"interest": []
},
{
"id": "b020cae2d52deaef",
"section": "papers",
"category": "几何与拓扑",
"title": "Positive scalar curvature and uniform codimension-two width",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Positive-scalar-curvature-and-uniform-codimension-two-width-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the quantitative continuous form of Gromov's scalar-curvature conjecture in every dimension n ≥ 4. Every complete connected smooth boundaryless n-manifold with scalar curvature at least one admits a continuous map to a simplicial complex of dimension at most $`n-2`$ whose entire fibers have diameter bounded only in terms of n. We also obtain the continuous macroscopic-dimension conclusion for universal covers of closed manifolds with positive scalar curvature in every dimension n ≥ 2.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Positive scalar curvature and uniform codimension-two width",
"titleZh": "正标量曲率与一致余维二宽度",
"details": {
"overview": "该稿件声称在每一维数n≥4证明了Gromov标量曲率猜想的定量连续形式：每个标量曲率至少为1的完备连通无边光滑n维流形，都存在到维数至多n−2的单纯复形的连续映射，且所有纤维的直径仅依赖于n而有界。摘要还称对正标量曲率闭流形的万有覆盖，在每一维数n≥2得到连续宏观维数结论。摘要未说明证明方法。若成立，将推进标量曲率与宏观维数方向的几何研究。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称证明Gromov标量曲率猜想的定量连续形式，适用于n≥4。",
"存在到至多n−2维单纯复形的连续映射，纤维直径仅由n控制。",
"另称对正标量曲率闭流形万有覆盖得到连续宏观维数结论。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "afe6f9a886955cac",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.9 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.9",
"date": "2026-09-23",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T18:00:16+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.9 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.9 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "af1b9a91a6b6418f",
"section": "news",
"category": "模型动态",
"title": "Harvey turns legal context into stronger drafts with GPT-6 Astra",
"summary": "官方发布摘要称，GPT-6 Astra 能生成结构更清晰、更贴合上下文的法律文档，从而让律师将精力集中在策略上。",
"url": "https://openai.com/index/harvey-from-context-to-confidence-with-astra",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T12:00:00+00:00",
"titleEn": "Harvey turns legal context into stronger drafts with GPT-6 Astra",
"titleZh": "Harvey 借助 GPT-6 Astra 将法律上下文转化为更佳草稿",
"details": {
"overview": "官方发布摘要称，GPT-6 Astra 能生成结构更清晰、更贴合上下文的法律文档，从而让律师将精力集中在策略上。该表述来自发布方，摘要未提供具体评测数据、对比基线或独立验证信息，实际效果需结合后续材料判断。",
"keyPoints": [
"摘要称 GPT-6 Astra 生成的法律文档更具结构性和上下文感知能力。",
"发布方称此举可让律师更专注于策略工作。",
"当前收录摘要未给出评测数据或独立验证细节。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "ad9021d6528ae7b8",
"section": "papers",
"category": "几何与拓扑",
"title": "Contact Fano manifolds and the LeBrun–Salamon conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the contact-Fano homogeneity conjecture and the Riemannian LeBrun–Salamon conjecture positively. Every smooth connected complex projective contact Fano manifold of complex dimension at least three, with its given contact distribution, is contact-isomorphic to the adjoint variety of a simple complex Lie algebra. Consequently, every closed connected smooth positive quaternionic-Kähler manifold of real dimension $`4m\\geq8`$ is homothetic to a compact symmetric Wolf space.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Contact Fano manifolds and the LeBrun–Salamon conjecture",
"titleZh": "接触Fano流形与LeBrun–Salamon猜想",
"details": {
"overview": "该稿件声称正面解决了接触Fano齐性猜想与Riemannian LeBrun–Salamon猜想。摘要称：每个复维数至少三的光滑连通复射影接触Fano流形，在给定接触分布下，都接触同构于某单复李代数的伴随簇；由此每个实维数4m≥8的闭连通光滑正四元数Kähler流形都位似于紧对称Wolf空间。当前收录摘要未给出证明细节。若成立，将统一接触几何与四元数Kähler几何中的两个重要分类问题。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称正面解决接触Fano齐性猜想，复维数至少三的接触Fano流形同构于伴随簇。",
"由此声称解决Riemannian LeBrun–Salamon猜想，正四元数Kähler流形位似于Wolf空间。",
"摘要未提供证明方法或独立验证信息。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "ad3ddadb8324cca5",
"section": "news",
"category": "行业新闻",
"title": "At AI Day Singapore, NVIDIA and Partners Showcase AI Advancements Across Southeast Asia",
"summary": "官方发布信息称，NVIDIA AI Day Singapore 于 9 月 22 日至 23 日在新加坡莱佛士城会议中心举行，参会者可体验实操培训、专家主导的会议和先进工具，以加速 AI 与高性能计算方面的工作。",
"url": "https://blogs.nvidia.com/blog/ai-day-singapore/",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "NVIDIA 官方博客",
"publishedAt": "2026-09-23T02:30:22+00:00",
"titleEn": "At AI Day Singapore, NVIDIA and Partners Showcase AI Advancements Across Southeast Asia",
"titleZh": "在新加坡 NVIDIA AI Day 上，NVIDIA 与合作伙伴展示东南亚 AI 进展",
"details": {
"overview": "官方发布信息称，NVIDIA AI Day Singapore 于 9 月 22 日至 23 日在新加坡莱佛士城会议中心举行，参会者可体验实操培训、专家主导的会议和先进工具，以加速 AI 与高性能计算方面的工作。活动期间，NVIDIA 及其合作伙伴展示东南亚地区的突破性 AI 进展。原文摘要在此处截断，未披露具体展示内容、合作方名单或产品细节。",
"keyPoints": [
"活动于 9 月 22 日至 23 日在新加坡莱佛士城会议中心举行。",
"参会者可体验实操培训、专家会议和 AI 与高性能计算工具。",
"NVIDIA 与合作伙伴展示东南亚地区 AI 进展，具体内容原文未完整披露。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "a9a518e229184581",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Smooth counterexamples to Yau's nodal upper bound in dimensions three and four",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a smooth metric on the three-sphere, arbitrarily close to the round metric in the smooth topology, and a smooth metric on $`S^2\\times\\mathbb T^2`$ for which sequences of exact real Laplace eigenfunctions have unbounded nodal measure divided by the square root of the eigenvalue. Each sequence belongs to one fixed metric. Thus the upper-bound part of Yau's nodal conjecture fails for smooth metrics in dimensions three and four.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Smooth counterexamples to Yau's nodal upper bound in dimensions three and four",
"titleZh": "三维和四维中Yau节点上界的光滑反例",
"details": {
"overview": "该稿件声称构造了三维球面上的光滑度量，在光滑拓扑下可任意接近圆度量，以及S²×T²上的光滑度量，使得精确实Laplace特征函数序列的节点测度除以特征值平方根无界；每个序列属于一个固定度量。摘要据此称Yau节点猜想的上界部分在三维和四维的光滑度量情形下不成立。当前收录摘要未给出构造细节。若成立，将对特征函数节点集几何测度研究产生重要影响。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件在S³上构造接近圆度量的光滑度量，使节点测度/√特征值无界。",
"在S²×T²上构造类似光滑度量反例。",
"据此声称Yau节点猜想上界部分在三维和四维光滑度量下失效。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何分析与谱几何",
"interest": []
},
{
"id": "a965d79c02beaeab",
"section": "papers",
"category": "几何与拓扑",
"title": "The Hilbert–Smith conjecture in every finite dimension",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Hilbert–Smith conjecture in every finite dimension: every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected Hausdorff second-countable finite-dimensional topological manifold without boundary is a Lie group.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Hilbert–Smith conjecture in every finite dimension",
"titleZh": "每个有限维数下的Hilbert–Smith猜想",
"details": {
"overview": "该稿件声称在每个有限维数下证明了Hilbert–Smith猜想：任何局部紧、第二可数Hausdorff群，若忠实且联合连续地作用在连通、Hausdorff、第二可数、有限维、无边的拓扑流形上，则该群是Lie群。摘要仅给出这一陈述，未说明证明策略或关键步骤。若成立，将解决拓扑群作用理论中长期悬而未决的核心问题。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称在每个有限维数证明Hilbert–Smith猜想。",
"结论为：满足给定作用条件的局部紧第二可数Hausdorff群必是Lie群。",
"摘要未交代证明方法，结论尚待独立审查。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "拓扑群与变换群",
"interest": []
},
{
"id": "a819f75045adf67a",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.156.0 发布",
"summary": "Codex CLI 0.156.0 发布说明列出多项新功能：可通过 /tui 选择可选全屏界面，支持记录搜索、鼠标选择和右键复制；语音对话默认启用，带 F8 切换、/voice settings 选择器及 Linux 和 Windows 音频运行时；新增 /usage 分析面板查看账户用量、token 总量及插件与技能活动；任务可按状态筛选并从代理命令中心创建工作树会话，工作树支持默认启用；新增六种终端主题，并可在回复中查看 Mermaid 图和公式。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.156.0",
"date": "2026-09-23",
"status": "CLI 稳定版本；桌面端功能另以对应公告为准。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T19:51:01+00:00",
"releaseChannel": "stable",
"titleEn": "Codex CLI 0.156.0 发布",
"titleZh": "Codex CLI 0.156.0 发布",
"details": {
"overview": "Codex CLI 0.156.0 发布说明列出多项新功能：可通过 /tui 选择可选全屏界面，支持记录搜索、鼠标选择和右键复制；语音对话默认启用，带 F8 切换、/voice settings 选择器及 Linux 和 Windows 音频运行时；新增 /usage 分析面板查看账户用量、token 总量及插件与技能活动；任务可按状态筛选并从代理命令中心创建工作树会话，工作树支持默认启用；新增六种终端主题，并可在回复中查看 Mermaid 图和公式。修复涉及流式回答保留、剪贴板转发、会话恢复、代理登录、语音播放及沙箱隔离等。",
"keyPoints": [
"新增可选全屏 TUI、默认启用的语音对话及 /usage 用量分析面板。",
"工作树支持默认启用，可从代理命令中心按状态筛选并创建会话。",
"修复流式回答保留、剪贴板转发、代理登录和沙箱隔离等问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "a7d2f1f21d5f4786",
"section": "papers",
"category": "代数几何",
"title": "The Bogomolov-Pop reconstruction theorem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Bogomolov–Pop reconstruction conjecture for function fields of transcendence degree at least two over arbitrary algebraically closed fields of characteristic different from ℓ. The pro-ℓ abelian-by-central datum determines the perfect closure and its constant field, with precisely the Frobenius and ℓ-adic unit ambiguities.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Bogomolov-Pop reconstruction theorem",
"titleZh": "Bogomolov–Pop重构定理",
"details": {
"overview": "该稿件声称对特征不等于ℓ的任意代数闭域上超越次数至少二的函数域，证明了Bogomolov–Pop重构猜想。摘要称pro-ℓ阿贝尔-by-中心数据决定完全闭包及其常数域，且恰好带有Frobenius与ℓ进单位的不确定性。摘要未说明证明技术。若成立，将为远阿贝尔几何中函数域的重构问题提供一般性结论。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称证明超越次数至少二的函数域上的Bogomolov–Pop重构猜想。",
"pro-ℓ阿贝尔-by-中心数据决定完全闭包与常数域。",
"不确定性恰为Frobenius与ℓ进单位；摘要未给证明细节。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何与远阿贝尔几何",
"interest": []
},
{
"id": "a5ee50c8f0c3c9e6",
"section": "papers",
"category": "组合数学与图论",
"title": "A counterexample to Ryser's covering conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Rysers-Covering-Conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every sufficiently large prime $`s\\equiv2\\pmod3`$ and every sufficiently large odd integer n, with the threshold depending on s, we construct an intersecting $`(s^n+1)`$-partite $`(s^n+1)`$-uniform hypergraph with covering number $`s^n+1`$. This disproves Ryser's covering conjecture in its intersecting case.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A counterexample to Ryser's covering conjecture",
"titleZh": "Ryser覆盖猜想的一个反例",
"details": {
"overview": "该稿件声称对每个充分大的素数s≡2 (mod 3)和每个充分大的奇数n（阈值依赖于s），构造了一个相交的(s^n+1)部、(s^n+1)一致超图，其覆盖数为s^n+1，从而在相交情形下否证Ryser覆盖猜想。当前收录摘要未给出构造细节或阈值估计。若成立，将对超图覆盖数与相交族研究产生重要影响。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件对充分大素数s≡2 (mod 3)与充分大奇数n构造相交超图。",
"该超图为(s^n+1)部、(s^n+1)一致，覆盖数为s^n+1。",
"据此声称在相交情形下否证Ryser覆盖猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "a5e26a24cca6b65b",
"section": "papers",
"category": "动力系统与遍历论",
"title": "Rokhlin's multiple-mixing problem for one transformation",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Rokhlins-multiple-mixing-problem-for-one-transformation-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every invertible mixing probability-preserving transformation is mixing of every finite order. Thus Rokhlin's multiple-mixing problem for a single transformation has an affirmative answer.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Rokhlin's multiple-mixing problem for one transformation",
"titleZh": "单个变换的Rokhlin多重混合问题",
"details": {
"overview": "该稿件声称每个可逆混合保概率变换都是任意有限阶混合的，从而对单个变换的Rokhlin多重混合问题给出肯定回答。摘要仅给出这一结论，未说明证明方法或与多重混合层级的关系。若成立，将解决遍历论中关于混合阶数的经典问题。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称每个可逆混合保概率变换都是任意有限阶混合的。",
"由此对单个变换的Rokhlin多重混合问题给出肯定回答。",
"摘要未提供证明思路或独立验证信息。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "遍历论与动力系统",
"interest": []
},
{
"id": "a570a4bd167b5f85",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Tracial projection methods and uniform property Gamma",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For a simple, separable, unital, infinite-dimensional, nuclear, stably finite C∗-algebra with traces, real rank zero of the uniform tracial ultrapower of its uniform tracial completion implies uniform property Γ. This answers Problem XXI of Schafhauser, Tikuisis and White affirmatively. Independently, strict comparison implies Jiang–Su absorption for simple, separable, unital, infinite-dimensional nuclear algebras, resolving the unital Toms–Winter conjecture. Under comparison tested on traces of finite target rank, we also obtain uniform property Γ and absorption for simple, separable, nuclear, stably projectionless algebras whose densely finite traces are all bounded and have a nonempty compact normalized base.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Tracial projection methods and uniform property Gamma",
"titleZh": "迹投影方法与一致性质Gamma",
"details": {
"overview": "该稿件讨论简单、可分、含单位、无限维、核、稳定有限的带迹C*代数。摘要称：其一致迹完备化的一致迹超幂若实秩为零，则蕴含一致性质Γ，从而肯定回答Schafhauser、Tikuisis与White的问题XXI；独立地，严格比较蕴含Jiang–Su吸收，解决含单位的Toms–Winter猜想；在有限目标秩迹上检验比较的条件下，还得到一类稳定无投影代数的一致性质Γ与吸收。摘要未给证明细节。需注意这是AI产生的研究手稿，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"一致迹超幂实秩为零蕴含一致性质Γ，回答Schafhauser–Tikuisis–White问题XXI。",
"严格比较蕴含Jiang–Su吸收，声称解决含单位Toms–Winter猜想。",
"对一类稳定无投影代数在附加比较条件下得到一致性质Γ与吸收。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "a44e395ab4283e5a",
"section": "papers",
"category": "代数与表示论",
"title": "An algebra of infinite little finitistic dimension",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An algebra of infinite little finitistic dimension",
"titleZh": "无限小有限投射维数的代数",
"details": {
"overview": "稿件构造了一个有限维复代数，其有限维模具有无界的有限投射维数。摘要表示，这一构造否证了小有限投射维数猜想。该猜想关注有限维代数上有限维模的有限投射维数是否有统一上界；若作者声称成立，则说明该上界并非普遍存在。材料仅给出摘要级结论，未提供构造细节或验证过程。",
"keyPoints": [
"构造有限维复代数，其有限维模的有限投射维数无界。",
"摘要称该结果否证小有限投射维数猜想。",
"仅见摘要结论，未给出构造与证明细节。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数学",
"interest": []
},
{
"id": "a336558cd9e7248d",
"section": "papers",
"category": "分析与偏微分方程",
"title": "An explicit obstruction to nuclear norm-ultrapower embeddings",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We give a negative answer to Kirchberg's norm-ultrapower embedding problem. We construct an explicit separable unital full group C∗-algebra that admits no unital embedding into Bω, for any nonzero unital nuclear C∗-algebra B and any free ultrafilter ω on ℕ. In particular, it does not embed unitally into $`\\mathcal O_2^\\omega`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An explicit obstruction to nuclear norm-ultrapower embeddings",
"titleZh": "核范数超幂嵌入的一个显式障碍",
"details": {
"overview": "稿件对Kirchberg的范数超幂嵌入问题给出否定回答。摘要称构造了一个显式可分的单位全群C*代数，使得对任意非零单位核C*代数B和ℕ上的任意自由超滤子ω，该代数都不能单位嵌入Bω；特别地，它不能单位嵌入O₂^ω。研究对象属于算子代数中的C*代数嵌入问题，作者声称的结果若成立，将为该嵌入问题提供具体反例。材料仅见摘要，未展开构造与论证。",
"keyPoints": [
"对Kirchberg范数超幂嵌入问题给出否定回答。",
"构造显式可分单位全群C*代数，不能单位嵌入任意Bω。",
"特别地不能单位嵌入O₂^ω，细节仅见摘要。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "a1ca555d1dfe60e9",
"section": "papers",
"category": "数学物理与量子信息",
"title": "The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We derive the nonlinear Boltzmann equation from a grand-canonical Newtonian gas with initial pair exclusion. We treat stable, finite-range radial potentials that are C2 except for an allowed repulsive singularity at the origin, and C1 initial probability densities with spatially summable Gaussian bounds on the density and its spatial gradient. All fixed-order rescaled factorial marginals converge in L1, uniformly throughout every finite interval on which the classical kinetic solution has a uniform Gaussian bound. The result allows attractive wells and dynamically formed clusters, without restrictions on the differential scattering cross-section.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals",
"titleZh": "正则动力学区间上稳定径向势的Boltzmann–Grad极限",
"details": {
"overview": "稿件从具有初始成对排斥的大正则牛顿气体出发推导非线性Boltzmann方程。摘要称处理稳定、有限程径向势，除原点允许排斥奇点外为C²，初值概率密度为C¹并满足空间可和的高斯界；在所有经典动力学解具有一致高斯界的有限区间上，固定阶重标度阶乘边缘分布L¹收敛。结果允许吸引势阱和动力学形成的团簇，且不限制微分散射截面。材料仅见摘要，未给出证明细节。",
"keyPoints": [
"从大正则牛顿气体推导非线性Boltzmann方程。",
"允许吸引势阱、动力学团簇及一般微分散射截面。",
"固定阶重标度阶乘边缘分布在L¹中一致收敛。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理",
"interest": []
},
{
"id": "a0a8899f0ba7e841",
"section": "papers",
"category": "组合数学与图论",
"title": "The Euclidean plane is not five-colorable",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every coloring of the Euclidean plane with five colors has a monochromatic unit-distance pair, with no regularity assumption on the color classes. Consequently, the chromatic number of the plane is either six or seven.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Euclidean plane is not five-colorable",
"titleZh": "欧几里得平面不可五着色",
"details": {
"overview": "稿件研究欧几里得平面染色问题。摘要称证明平面任意五染色必存在同色单位距离点对，且不对色类作正则性假设；由此平面色数只能为六或七。该结果针对单位距离图的染色数，作者声称将此前已知下界推进到六。材料仅提供摘要级陈述，未给出证明构造或独立验证信息。",
"keyPoints": [
"证明平面任意五染色存在同色单位距离点对。",
"不假设色类具有任何正则性。",
"推论平面色数为六或七。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "9d44c635cbc7e0b7",
"section": "papers",
"category": "代数与表示论",
"title": "A Counterexample to Kurosh’s Division-Ring Problem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a countable division ring of characteristic zero that is algebraic over its center, generated by two elements as an algebra over that center, and infinite-dimensional over it. This gives a negative answer to the Kurosh problem for division rings.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A Counterexample to Kurosh’s Division-Ring Problem",
"titleZh": "Kurosh除环问题的一个反例",
"details": {
"overview": "稿件构造了一个可数、特征为零的除环，它在其中心上代数、作为该中心上的代数由两个元素生成，且在该中心上无限维。摘要表示这否定了除环的Kurosh问题。该问题通常关注代数性是否迫使有限维；作者声称的反例说明在除环情形下答案是否定的。材料仅见摘要，未提供构造步骤与验证细节。",
"keyPoints": [
"构造可数特征零除环，在中心上代数且无限维。",
"该除环作为中心上代数由两个元素生成。",
"摘要称其否定除环的Kurosh问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数学",
"interest": []
},
{
"id": "9aa77404ad142c3f",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Relative independence of the separable quotient problem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Relative-independence-of-the-separable-quotient-problem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "The separable quotient problem asks whether every infinite-dimensional Banach space has a separable infinite-dimensional quotient. We prove that this statement is independent of ZFC, relative to the consistency of ZFC with a measurable cardinal. This holds over both the real and complex fields. For spaces of norm density ℵ1, we obtain independence relative to the consistency of ZFC alone.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Relative independence of the separable quotient problem",
"titleZh": "可分商问题的相对独立性",
"details": {
"overview": "可分商问题问是否每个无限维Banach空间都有可分无限维商空间。稿件摘要称，在ZFC与可测基数一致的前提下，该命题独立于ZFC；实域与复域情形均如此。对于范数密度为ℵ₁的空间，作者声称仅需ZFC的一致性即可得到独立性。研究属于泛函分析与集合论交叉领域，材料仅见摘要，未展开力迫构造或证明。",
"keyPoints": [
"声称可分商问题相对ZFC独立，需可测基数一致性。",
"实域与复域情形均适用。",
"范数密度ℵ₁空间仅需ZFC一致性。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "泛函分析与集合论",
"interest": []
},
{
"id": "98ae5d212a1e058e",
"section": "papers",
"category": "概率与统计",
"title": "SLE3 universality for weak finite-range Ising interactions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every sufficiently small, square-symmetric finite-range perturbation of the planar Ising contour energy has a domain-independent inverse temperature at which its spin interface converges to chordal SLE3. The result allows interactions of either sign, arbitrary admissible exterior contours, and uniformly approximated Jordan domains. Convergence holds for the full oriented curve law in uniform distance modulo increasing reparametrization.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "SLE3 universality for weak finite-range Ising interactions",
"titleZh": "弱有限程Ising相互作用的SLE₃普适性",
"details": {
"overview": "稿件研究平面Ising轮廓能量的充分小、平方对称有限程扰动。摘要称存在与区域无关的逆温度，使自旋界面收敛到弦SLE₃；结果允许相互作用取正负号、任意容许外轮廓及一致逼近的Jordan区域。收敛按完整定向曲线律在模递增重参数化的均匀距离下成立。材料仅见摘要，未给出证明细节或独立验证。",
"keyPoints": [
"对平面Ising轮廓能量的弱有限程扰动证明SLE₃收敛。",
"存在与区域无关的逆温度，允许正负相互作用。",
"收敛针对完整定向曲线律，模递增重参数化。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与统计物理",
"interest": []
},
{
"id": "960d3479b03cfa30",
"section": "papers",
"category": "理论计算机科学",
"title": "Integer multiplication below n log n",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We give a deterministic algorithm that multiplies two n-bit integers in $`O(n(\\lg n)^{1-\\kappa})`$ worst-case time, with $`\\kappa=2^{-182}`$, on one fixed finite-alphabet Turing machine with a fixed finite number of one-dimensional tapes. The algorithm is exact for every input length and disproves the $`n\\log n`$ optimality conjecture of Schönhage and Strassen in this model.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Integer multiplication below n log n",
"titleZh": "低于n log n的整数乘法",
"details": {
"overview": "稿件给出一个确定性算法，在固定有限字母表、固定有限条一维带的单台图灵机上，以O(n(lg n)^{1−κ})最坏时间乘两个n位整数，其中κ=2^{−182}。摘要称算法对所有输入长度精确，并在该模型下否证Schönhage–Strassen的n log n最优性猜想。研究属于算法与计算复杂性，材料仅见摘要，未提供算法描述与复杂度证明细节。",
"keyPoints": [
"给出确定性整数乘法算法，最坏时间O(n(lg n)^{1−κ})。",
"κ=2^{−182}，在固定有限带图灵机模型下成立。",
"摘要称否证Schönhage–Strassen的n log n最优性猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算法与计算复杂性",
"interest": []
},
{
"id": "95d4f3058dc64161",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.10 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.10",
"date": "2026-09-23",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T22:07:05+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.10 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.10 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "95b3e19c83639254",
"section": "papers",
"category": "几何与拓扑",
"title": "Purely cosmetic surgery on knots in the three-sphere",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the purely cosmetic surgery conjecture for knots in the three-sphere. Distinct Dehn surgery slopes on a nontrivial smooth knot never give orientation-preservingly homeomorphic manifolds.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Purely cosmetic surgery on knots in the three-sphere",
"titleZh": "三维球面中纽结的纯美容手术",
"details": {
"overview": "稿件研究三维球面中纽结的Dehn手术。摘要称证明了纯美容手术猜想：非平凡光滑纽结上不同的Dehn手术斜率不会给出保定向同胚的流形。该问题属于低维拓扑中纽结手术理论，作者声称的结果若成立，将排除同一纽结不同斜率产生同胚流形的情形。材料仅见摘要，未给出证明细节或独立审查信息。",
"keyPoints": [
"声称证明三维球面中纽结的纯美容手术猜想。",
"不同Dehn手术斜率不给出保定向同胚流形。",
"对象为非平凡光滑纽结，细节仅见摘要。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "950d3d2bce1f0e8c",
"section": "papers",
"category": "代数与表示论",
"title": "Thompson's group F is nonamenable",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that Thompson's group F is nonamenable. This confirms Geoghegan's conjecture and resolves the amenability problem for F.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Thompson's group F is nonamenable",
"titleZh": "Thompson群F非顺从",
"details": {
"overview": "稿件研究Thompson群F的顺从性问题。摘要称证明F非顺从，从而确认Geoghegan猜想并解决F的顺从性问题。该群是几何群论中的经典对象，其顺从性长期未决；作者声称的结果若成立，将给出否定答案。材料仅提供摘要级陈述，未给出证明思路、构造或独立验证信息。",
"keyPoints": [
"摘要称证明Thompson群F非顺从。",
"声称确认Geoghegan猜想并解决F的顺从性问题。",
"仅见摘要结论，未提供证明细节。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何群论",
"interest": []
},
{
"id": "94ccd8e223b1f0de",
"section": "papers",
"category": "几何与拓扑",
"title": "A single-lattice covering bound of order n log n",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-single-lattice-covering-bound-of-order-n-log-n-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every convex body in ℝn, n ≥ 2, admits a covering by translates along one full-rank lattice with density at most $`Cn\\log n`$, for an absolute constant C. No symmetry or boundary regularity is assumed.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A single-lattice covering bound of order n log n",
"titleZh": "n log n阶的单格覆盖界",
"details": {
"overview": "稿件研究ℝⁿ中凸体的格覆盖问题。摘要称对任意n≥2的凸体，存在沿一个满秩格平移的覆盖，密度至多Cn log n，其中C为绝对常数；不假设对称性或边界正则性。该结果给出单格覆盖密度的一个阶为n log n的上界。材料仅见摘要，未说明常数取值、证明方法或与已有界的比较细节。",
"keyPoints": [
"任意ℝⁿ凸体可沿一个满秩格平移覆盖。",
"覆盖密度上界为Cn log n，C为绝对常数。",
"不假设凸体对称性或边界正则性。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "凸几何与离散几何",
"interest": []
},
{
"id": "935d551f044eecfc",
"section": "papers",
"category": "概率与统计",
"title": "Exponential decay in two-dimensional classical O(n) models",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove exponential decay of two-point correlations for the classical nearest-neighbor $`O(n)`$ model on the square lattice, for every n ≥ 3 and every finite positive inverse temperature. The estimate is uniform over finite free-boundary subgraphs and bounded nonnegative edge strengths. This resolves positively the all-temperature exponential spin-decay conjecture for these models.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Exponential decay in two-dimensional classical O(n) models",
"titleZh": "二维经典O(n)模型中的指数衰减",
"details": {
"overview": "稿件研究方格上经典最近邻O(n)模型。摘要称对每个n≥3和每个有限正逆温度，证明两点关联指数衰减；估计在有限自由边界子图和有界非负边强度上一致。作者声称这正面解决了这些模型的全温度指数自旋衰减猜想。材料仅见摘要，未给出证明方法或独立验证信息。",
"keyPoints": [
"对二维方格O(n)模型证明两点关联指数衰减。",
"适用于每个n≥3及每个有限正逆温度。",
"估计在有限自由边界子图与有界边强度上一致。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与统计物理",
"interest": []
},
{
"id": "9314010ae62e792c",
"section": "papers",
"category": "代数几何",
"title": "The abelianity conjecture for special compact Kähler manifolds",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the fundamental group of every special compact Kähler manifold is virtually abelian, resolving Campana's abelianity conjecture in all dimensions. In particular, every smooth compact connected Kähler manifold of Kodaira dimension zero has virtually abelian ordinary fundamental group.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The abelianity conjecture for special compact Kähler manifolds",
"titleZh": "特殊紧Kähler流形的阿贝尔性猜想",
"details": {
"overview": "稿件提出证明：每个特殊紧Kähler流形的基本群是几乎阿贝尔的，从而在所有维数上解决了Campana的阿贝尔性猜想。摘要表示，作为推论，每个Kodaira维数为零的光滑紧连通Kähler流形具有几乎阿贝尔的普通基本群。该结果属于复几何与几何群论交叉领域，若成立将为特殊流形的拓扑结构提供统一描述。",
"keyPoints": [
"证明特殊紧Kähler流形的基本群几乎阿贝尔，解决Campana猜想。",
"推论：Kodaira维数为零的光滑紧连通Kähler流形基本群几乎阿贝尔。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "8ed16c1296e86191",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Asymptotically minimal maxima of real Littlewood polynomials",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the minimum possible maximum modulus on the unit circle of a polynomial with N consecutive real coefficients in $`\\{-1,1\\}`$ is $`(1+o(1))\\sqrt N`$, as N tends to infinity through all integers. This disproves the real-sign analogue of Erdős's fixed relative-gap conjecture. As a consequence, the largest binary merit factor at length N tends to infinity through all integer lengths, disproving Turyn's conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Asymptotically minimal maxima of real Littlewood polynomials",
"titleZh": "实Littlewood多项式的渐近极小极大值",
"details": {
"overview": "稿件研究具有N个连续实系数（取值于{-1,1}）的多项式在单位圆上的最大模，证明其最小可能值当N趋于无穷时渐近为(1+o(1))√N。摘要表示，这否定了Erdős固定相对间隙猜想的实符号类比，并推出最大二进制优值因子随长度趋于无穷，从而否定Turyn猜想。该工作涉及多项式极值问题与组合设计。",
"keyPoints": [
"证明最小最大模渐近为√N，否定Erdős猜想的实符号版本。",
"推出最大二进制优值因子趋于无穷，否定Turyn猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "8e74872fb1c686e6",
"section": "papers",
"category": "概率与统计",
"title": "The curve scaling limit of half-plane double dimers",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the complete double-dimer loop ensemble for the Temperleyan square lattice in the upper half-plane converges to nested CLE4. The convergence holds along the full mesh limit and matches every macroscopic loop as an unparametrized curve. This resolves the half-plane Temperleyan form of the double-dimer CLE4 scaling-limit conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The curve scaling limit of half-plane double dimers",
"titleZh": "半平面双二聚体的曲线标度极限",
"details": {
"overview": "稿件研究上半平面Temperleyan方格上的完全双二聚体环系综，证明其收敛到嵌套CLE4。摘要表示，收敛沿完整网格极限成立，且每个宏观环作为无参数曲线匹配，从而解决了双二聚体CLE4标度极限猜想的半平面Temperleyan形式。该结果属于概率论与统计物理中的随机几何。",
"keyPoints": [
"证明半平面Temperleyan方格双二聚体环系综收敛到嵌套CLE4。",
"收敛沿完整网格极限，每个宏观环作为无参数曲线匹配。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "8e5f733e8bd15eec",
"section": "papers",
"category": "概率与统计",
"title": "Directional transience implies ballisticity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Directional-transience-implies-ballisticity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that almost-sure transience in a fixed direction implies a deterministic limiting velocity with positive projection in that direction for nearest-neighbor random walks in independent and identically distributed uniformly elliptic environments on ℤd, d ≥ 2. This resolves the ballisticity conjecture positively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Directional transience implies ballisticity",
"titleZh": "方向暂态蕴含弹道性",
"details": {
"overview": "稿件研究ℤd（d≥2）上独立同分布均匀椭圆环境中的最近邻随机游走，证明若几乎必然在固定方向上暂态，则存在确定性极限速度且在该方向投影为正。摘要表示，这正面解决了弹道性猜想。该结果连接随机环境中的方向行为与渐近速度，属于概率论与数学物理。",
"keyPoints": [
"证明固定方向几乎必然暂态蕴含正投影的确定性极限速度。",
"适用于独立同分布均匀椭圆环境中的最近邻随机游走。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "8c61d002870be337",
"section": "papers",
"category": "几何与拓扑",
"title": "Harmonic heights and the Artin K(pi,1) conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Harmonic-heights-and-the-Artin-K-pi-1-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the standard Salvetti complex of every Artin group with finitely many standard generators is aspherical. This resolves the Artin $`K(\\pi,1)`$ conjecture in finite rank.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Harmonic heights and the Artin K(pi,1) conjecture",
"titleZh": "调和高度与Artin K(π,1)猜想",
"details": {
"overview": "稿件研究有限多个标准生成元的Artin群，证明其标准Salvetti复形是 aspherical 的。摘要表示，这解决了有限秩的Artin K(π,1)猜想。该结果属于几何群论与拓扑学，若成立将为Artin群的分类空间性质提供一般性结论。",
"keyPoints": [
"证明有限生成Artin群的标准Salvetti复形是aspherical。",
"解决有限秩的Artin K(π,1)猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "8b5a387ad5fd90d3",
"section": "news",
"category": "行业新闻",
"title": "Sam Altman’s remarks at the United Nations Security Council",
"summary": "官方发布摘要称，OpenAI CEO Sam Altman 在联合国安理会发表讲话，讨论 AI 安全、人类控制以及国际合作。",
"url": "https://openai.com/index/sam-altman-un-security-council-remarks",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T12:00:00+00:00",
"titleEn": "Sam Altman’s remarks at the United Nations Security Council",
"titleZh": "Sam Altman 在联合国安理会的发言",
"details": {
"overview": "官方发布摘要称，OpenAI CEO Sam Altman 在联合国安理会发表讲话，讨论 AI 安全、人类控制以及国际合作。摘要未披露发言的具体主张、政策建议或各方反应，相关内容需以完整发言记录为准。",
"keyPoints": [
"OpenAI CEO Sam Altman 在联合国安理会发表讲话。",
"发言主题包括 AI 安全、人类控制与国际合作。",
"摘要未披露具体政策主张或各方反应。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "8af3f1efd561d296",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Sharp one-dimensional Lieb–Thirring constants",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve affirmatively the remaining cases of the scalar one-dimensional Lieb–Thirring conjecture: for every $`\\frac12\\lt \\gamma\\lt \\frac32`$, the optimal constant is the one-bound-state constant. The estimate holds for every nonnegative potential in $`L^{\\gamma+1/2}(\\mathbb R)`$, with all negative eigenvalues included.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Sharp one-dimensional Lieb–Thirring constants",
"titleZh": "尖锐一维Lieb–Thirring常数",
"details": {
"overview": "稿件研究一维标量Lieb–Thirring猜想，声称对每个1/2<γ<3/2，最优常数是单束缚态常数。摘要表示，该估计对L^{γ+1/2}(ℝ)中每个非负势成立，并包含所有负特征值。这解决了该猜想剩余情形，属于泛函分析与数学物理中的谱不等式。",
"keyPoints": [
"对1/2<γ<3/2证明最优常数为单束缚态常数。",
"估计适用于L^{γ+1/2}(ℝ)中非负势并包含所有负特征值。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "8954a915bfeb3e13",
"section": "papers",
"category": "代数与表示论",
"title": "An infinite finitely presented simple amenable group",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-Infinite-Finitely-Presented-Simple-Amenable-Group-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct an infinite finitely presented simple amenable group, giving a positive answer to the finite-presentation existence question for simple amenable groups.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An infinite finitely presented simple amenable group",
"titleZh": "一个无限有限表示单可均群",
"details": {
"overview": "稿件构造了一个无限、有限表示、单且可均的群，摘要表示这正面回答了单可均群有限表示存在性问题。该结果属于群论，若成立将连接可均性、单性与有限表示性等群论性质。",
"keyPoints": [
"构造无限有限表示单可均群。",
"正面回答单可均群有限表示存在性问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "88ce0cad410612a6",
"section": "papers",
"category": "代数几何",
"title": "Fujita's freeness conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Fujita's freeness conjecture. If X is a smooth complex projective variety of dimension n and L is an ample line bundle, then $`K_X+mL`$ is globally generated for every integer $`m\\geq n+1`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Fujita's freeness conjecture",
"titleZh": "Fujita自由性猜想",
"details": {
"overview": "稿件研究光滑复射影簇X（维数n）上的丰沛线丛L，证明K_X+mL对每个整数m≥n+1全局生成。摘要表示，这证明了Fujita自由性猜想。该结果属于代数几何中的正性理论，若成立将给出伴随线丛全局生成的一般维数界。",
"keyPoints": [
"证明K_X+mL对m≥n+1全局生成。",
"解决Fujita自由性猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "83df901c51ba9db0",
"section": "papers",
"category": "代数几何",
"title": "Canonical ampleness of compact hyperbolic Kähler manifolds",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every compact connected Kähler manifold of positive complex dimension containing no nonconstant entire curve has ample canonical bundle and is projective. This resolves positively Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler category.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Canonical ampleness of compact hyperbolic Kähler manifolds",
"titleZh": "紧双曲Kähler流形的典范丰沛性",
"details": {
"overview": "稿件研究正复维数、不含非常数整曲线的紧连通Kähler流形，证明其典范丛丰沛且流形射影。摘要表示，这正面解决了光滑紧Kähler范畴中的Kobayashi典范丰沛性猜想。该结果属于复几何与双曲性理论。",
"keyPoints": [
"证明不含非常数整曲线的紧连通Kähler流形典范丛丰沛且射影。",
"正面解决光滑紧Kähler范畴的Kobayashi典范丰沛性猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "8325038668ecf90c",
"section": "papers",
"category": "理论计算机科学",
"title": "Beyond the Square-Root Exponent for Depth-Three Boolean Circuits",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Beyond-the-Square-Root-Exponent-for-Depth-Three-Boolean-Circuits-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a language in deterministic polynomial time whose n-bit membership function requires $`2^{\\omega(\\sqrt n)}`$ gates in an unbounded-fan-in OR–AND–OR circuit. The bound holds at every sufficiently large input length and counts all gates, including the bottom layer.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Beyond the Square-Root Exponent for Depth-Three Boolean Circuits",
"titleZh": "深度三布尔电路超越平方根指数",
"details": {
"overview": "稿件构造一个确定性多项式时间语言，其n位成员函数在无界扇入OR–AND–OR电路中需要2^{ω(√n)}个门。摘要表示，该界在每个充分大输入长度成立，并计数所有门包括底层。该结果属于计算复杂性理论中的电路下界。",
"keyPoints": [
"构造确定性多项式时间语言，其成员函数需2^{ω(√n)}个门。",
"下界适用于无界扇入OR–AND–OR电路并计数所有门。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "理论计算机科学",
"interest": []
},
{
"id": "8207eb295c262a21",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.156.1 发布",
"summary": "Codex CLI 0.156.1 为 0.156.0 的热修复版本。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.156.1",
"date": "2026-09-23",
"status": "CLI 稳定版本；桌面端功能另以对应公告为准。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-23T02:41:36+00:00",
"releaseChannel": "stable",
"titleEn": "Codex CLI 0.156.1 发布",
"titleZh": "Codex CLI 0.156.1 发布",
"details": {
"overview": "Codex CLI 0.156.1 为 0.156.0 的热修复版本。发布说明称，用户可在模型选择器中选择 GPT-6 Sol 或 GPT-6 Luna，触发速率限制时的切换提示现在推荐 GPT-6 Luna。该版本主要将上述两个模型加入模型目录，未提及其他功能变更。",
"keyPoints": [
"0.156.1 为 0.156.0 的热修复版本。",
"模型选择器新增 GPT-6 Sol 和 GPT-6 Luna。",
"速率限制切换提示改为推荐 GPT-6 Luna。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "80a37b1527f1167a",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Subpolynomial dimension reduction in Lp",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Subpolynomial-dimension-reduction-in-Lp-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed $`1\\lt p\\lt \\infty`$ and D > 1, every n-point subset of a real Lp space embeds into $`\\ell_p^d`$ with distortion at most D and subpolynomial dimension $`d=n^{o(1)}`$. The target has the same exponent p, and the embedding need not be linear.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Subpolynomial dimension reduction in Lp",
"titleZh": "Lp中的次多项式维数约化",
"details": {
"overview": "稿件研究实Lp空间的n点子集，证明对每个固定11，可嵌入到ℓ_p^d，失真至多D且维数d=n^{o(1)}。摘要表示，目标空间具有相同指数p，且嵌入不必线性。该结果属于度量几何与泛函分析中的维数约化。",
"keyPoints": [
"证明n点Lp子集可嵌入ℓ_p^d，失真至多D且d=n^{o(1)}。",
"目标空间指数p相同，嵌入不必线性。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "802c88dad6c3f23b",
"section": "news",
"category": "模型动态",
"title": "Gemini 3.8 text-to-speech says hello",
"summary": "现有材料仅有标题“Gemini 3.8 text-to-speech says hello”，摘要与原文内容均未提供具体信息，无法确认该文本转语音功能的具体能力、可用范围或发布时间。",
"url": "https://deepmind.google/blog/say-hello-to-gemini-38-text-to-speech/",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "Google DeepMind",
"publishedAt": "2026-09-23T15:25:14+00:00",
"titleEn": "Gemini 3.8 text-to-speech says hello",
"titleZh": "Gemini 3.8 文本转语音亮相",
"details": {
"overview": "现有材料仅有标题“Gemini 3.8 text-to-speech says hello”，摘要与原文内容均未提供具体信息，无法确认该文本转语音功能的具体能力、可用范围或发布时间。以下要点仅基于标题，信息明显不足。",
"keyPoints": [
"标题指向 Gemini 3.8 的文本转语音功能。",
"材料未提供功能细节、可用范围或发布时间。"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "7f21ab5f275d50bd",
"section": "papers",
"category": "分析与偏微分方程",
"title": "The complete Crouzeix theorem: optimal similarity and a common positive boundary representation",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-complete-Crouzeix-theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the complete Crouzeix conjecture by proving the sharp constant-two numerical-range inequality for every bounded operator on a complex Hilbert space and every matrix-valued polynomial. No separability assumption is needed. The closure of the numerical range is a complete 2-spectral set, and the bound extends to finite matrix-valued functions holomorphic near that closure. For a finite matrix and a bounded convex domain containing its numerical range with regular real-analytic Jordan boundary, the optimal similarity making its conformal disk image contractive is attained with condition number at most two. For the similar matrix, one continuous positive boundary density of mass the identity represents the evaluation of every matrix-valued function holomorphic near the closed domain.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The complete Crouzeix theorem: optimal similarity and a common positive boundary representation",
"titleZh": "完整Crouzeix定理：最优相似与公共正边界表示",
"details": {
"overview": "稿件研究复Hilbert空间上有界算子和矩阵值多项式，证明尖锐常数二的数值域不等式，无需可分性假设。摘要表示，数值域闭包是完全2-谱集，界可延拓到闭包附近全纯的有限矩阵值函数；对有限矩阵和包含数值域的有界凸域，最优相似的条件数至多二，并存在连续正边界密度表示全纯函数取值。该工作解决完整Crouzeix猜想。",
"keyPoints": [
"证明常数二的数值域不等式对任意有界算子和矩阵值多项式成立。",
"数值域闭包是完全2-谱集，界延拓到全纯矩阵值函数。",
"最优相似条件数至多二，并给出公共正边界表示。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "7d1ff206cfec2cfc",
"section": "papers",
"category": "组合数学与图论",
"title": "The circulant Hadamard conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-circulant-Hadamard-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the circulant Hadamard conjecture: a real circulant Hadamard matrix has order 1 or 4. As a consequence, Barker sequences of length greater than one exist exactly at lengths 2, 3, 4, 5, 7, 11, 13, proving the Barker-sequence conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The circulant Hadamard conjecture",
"titleZh": "循环Hadamard猜想",
"details": {
"overview": "该稿件声称证明了循环Hadamard猜想：实循环Hadamard矩阵的阶只能是1或4。摘要表示，由此可推出长度大于1的Barker序列恰好存在于长度2、3、4、5、7、11、13，从而证明Barker序列猜想。研究对象是组合设计与序列理论中的经典猜想，若成立将统一解决两个长期问题；但该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"稿件声称实循环Hadamard矩阵的阶仅为1或4",
"由此推出Barker序列长度限于2、3、4、5、7、11、13",
"结论同时覆盖循环Hadamard猜想与Barker序列猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "7cee73683971a2a4",
"section": "papers",
"category": "几何与拓扑",
"title": "A torsion-free hyperbolic group that is not residually finite",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question for hyperbolic groups negatively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A torsion-free hyperbolic group that is not residually finite",
"titleZh": "一个非剩余有限的无挠双曲群",
"details": {
"overview": "该稿件构造了一个无挠的字双曲群，并声称它不是剩余有限的，从而对双曲群的剩余有限性问题给出否定回答。研究对象属于几何群论中的双曲群与剩余有限性。摘要仅给出构造与否定结论，未展开构造细节或验证方式；该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"构造无挠字双曲群作为反例",
"声称该群不是剩余有限的",
"否定双曲群剩余有限性的一般问题"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何群论",
"interest": []
},
{
"id": "7c8ee3e8e946aeb4",
"section": "news",
"category": "行业新闻",
"title": "Sakeena Fiza Helps NVIDIA Hardware Succeed at Scale",
"summary": "该报道介绍 NVIDIA 验证工程师 Sakeena Fiza 的工作。",
"url": "https://blogs.nvidia.com/blog/nvidia-life-sakeena-fiza/",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "NVIDIA 官方博客",
"publishedAt": "2026-09-23T15:00:32+00:00",
"titleEn": "Sakeena Fiza Helps NVIDIA Hardware Succeed at Scale",
"titleZh": "Sakeena Fiza 助力 NVIDIA 硬件实现规模化成功",
"details": {
"overview": "该报道介绍 NVIDIA 验证工程师 Sakeena Fiza 的工作。她将验证工作比作侦探查案，称验证工程师要照亮系统的每个角落，拿到系统后首先思考如何找出问题。原文仅呈现这一人物视角的开头，未展开具体技术方法或成果数据，因此可确认的信息有限。",
"keyPoints": [
"介绍 NVIDIA 验证工程师 Sakeena Fiza 的岗位视角",
"以侦探比喻说明验证工程师排查系统隐患的工作方式",
"原文未展开具体验证方法或量化成果"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "7b56950bdca1b1b1",
"section": "papers",
"category": "代数几何",
"title": "An explicit failure of complex affine-space cancellation",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct an explicit integral complex affine fourfold X with $`X\\times\\mathbb A^1\\cong\\mathbb A^5`$ but $`X\\not\\cong\\mathbb A^4`$. This gives a negative answer to Zariski's affine-space cancellation problem over ℂ in dimension four. The same construction disproves the Stable Coordinate Conjecture in ambient dimension five and yields smooth 𝔸3-fibrations over 𝔸1 and 𝔸2 that are not Zariski-locally trivial. These fibrations disprove the Dolgachev–Weisfeiler affine-fibration conjecture over these bases.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An explicit failure of complex affine-space cancellation",
"titleZh": "复仿射空间消去性的一个显式失败",
"details": {
"overview": "该稿件构造了一个显式的整复仿射四维簇X，满足X×A^1同构于A^5但X不同构于A^4，声称由此否定Zariski仿射空间消去问题在ℂ上维数四的情形。摘要还表示同一构造否证五维环境下的稳定坐标猜想，并给出在A^1与A^2上非Zariski局部平凡的平滑A^3纤维化，从而否定这些基上的Dolgachev–Weisfeiler仿射纤维化猜想。手稿为AI产生，未经独立审查。",
"keyPoints": [
"构造X×A^1≅A^5而X≇A^4的复仿射四维簇",
"声称否定ℂ上维数四的Zariski消去问题",
"同一构造否证稳定坐标猜想与Dolgachev–Weisfeiler猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "79f5530fbf5029b9",
"section": "papers",
"category": "几何与拓扑",
"title": "A finitely generated counterexample to the Eilenberg–Ganea conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A finitely generated counterexample to the Eilenberg–Ganea conjecture",
"titleZh": "Eilenberg–Ganea猜想的一个有限生成反例",
"details": {
"overview": "该稿件构造了一个有限生成、剩余有限的群，其整系数上同调维数为二而几何维数为三，声称由此否证Eilenberg–Ganea猜想。研究对象涉及群的同调维数与几何维数之间的关系。摘要仅给出反例的基本性质，未说明构造方法或验证细节；该手稿为AI产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"构造有限生成剩余有限群作为反例",
"该群上同调维数为二、几何维数为三",
"声称否证Eilenberg–Ganea猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何群论",
"interest": []
},
{
"id": "791aa94f5608bb5a",
"section": "papers",
"category": "数理逻辑与基础",
"title": "Choiceless polynomial time with counting does not capture polynomial time",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that choiceless polynomial time with counting does not capture polynomial time on unordered finite structures, confirming the noncapture conjecture of Blass, Gurevich and Shelah. A linear-consistency query over 𝔽3 in a fixed binary vocabulary is decidable in polynomial time but not in the full counting formalism.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Choiceless polynomial time with counting does not capture polynomial time",
"titleZh": "带计数的无选择多项式时间不能刻画多项式时间",
"details": {
"overview": "该稿件声称证明了带计数的无选择多项式时间在无序有限结构上不能刻画多项式时间，从而证实Blass、Gurevich与Shelah提出的非刻画猜想。摘要表示，在一个固定二元词汇表上关于𝔽3的线性一致性查询可在多项式时间内判定，但不能在完整计数形式体系中表达。研究对象属于有限模型论与描述复杂性；手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"声称带计数的无选择多项式时间不刻画多项式时间",
"给出𝔽3上线性一致性查询作为分离例子",
"证实Blass–Gurevich–Shelah非刻画猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "描述复杂性理论",
"interest": []
},
{
"id": "783c2a60e49203d8",
"section": "papers",
"category": "几何与拓扑",
"title": "Almost-everywhere regularity of stationary integral varifolds",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Almost-everywhere-regularity-of-stationary-integral-varifolds-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the almost-everywhere regularity conjecture of Brena, Decio, and De Lellis for stationary integral varifolds of arbitrary positive dimension and codimension in Euclidean open sets. The singular set has zero measure in the dimension of the varifold: near almost every support point, the varifold is a constant positive integer multiple of a smooth embedded minimal submanifold. The corresponding statement also holds on round spheres.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Almost-everywhere regularity of stationary integral varifolds",
"titleZh": "稳定整变流形的几乎处处正则性",
"details": {
"overview": "该稿件声称解决了Brena、Decio与De Lellis关于欧氏开集中任意正维数与余维数的稳定整变流形的几乎处处正则性猜想。摘要表示，奇异集在变流形维数下测度为零：在几乎每个支撑点附近，变流形是光滑嵌入极小子流形的正常数正整数倍；相应结论在圆球面上也成立。研究对象属于几何测度论中的极小曲面与变流形正则性理论；手稿为AI产生，未经独立审查。",
"keyPoints": [
"奇异集在变流形维数下测度为零",
"几乎处处局部为光滑嵌入极小子流形的整数倍",
"结论同时推广到圆球面情形"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何测度论",
"interest": []
},
{
"id": "7808215132c3579c",
"section": "papers",
"category": "代数与表示论",
"title": "An explicit counterexample to the Auslander-Reiten conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove the Auslander–Reiten conjecture for Artin algebras. We construct a finite-dimensional algebra Λ over $`k=\\mathbb F_2(q,H_1,H_2)`$ and a finite-dimensional nonprojective left module Z such that $`\\mathop{\\mathrm{Ext}}\\nolimits ^i_\\Lambda(Z,Z)=\\mathop{\\mathrm{Ext}}\\nolimits ^i_\\Lambda(Z,\\Lambda)=0`$ for every i > 0. The module is Gorenstein-projective, so the same example also disproves the Gorenstein-projective conjecture. Both counterexamples persist after every extension of k.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An explicit counterexample to the Auslander-Reiten conjecture",
"titleZh": "Auslander–Reiten猜想的一个显式反例",
"details": {
"overview": "该稿件声称否证了Artin代数上的Auslander–Reiten猜想。摘要表示，在域k=𝔽2(q,H1,H2)上构造有限维代数Λ及有限维非投射左模Z，使得对所有i>0都有Ext^i_Λ(Z,Z)=0与Ext^i_Λ(Z,Λ)=0；该模是Gorenstein投射的，因此同一例子也否证Gorenstein投射猜想，且两个反例在k的任意扩张后仍成立。手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"构造满足所有正次Ext消失的非投射模Z",
"同一例子否证Auslander–Reiten与Gorenstein投射猜想",
"反例在基域任意扩张后仍成立"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数表示论",
"interest": []
},
{
"id": "7619d8fe1516a876",
"section": "papers",
"category": "代数与表示论",
"title": "A Torsion-Free Group Algebra with Zero Divisors",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove Kaplansky's zero-divisor conjecture by constructing a finitely presented torsion-free group G for which $`\\mathbb F_2[G]`$ has nonzero zero divisors. The group admits a finite two-dimensional classifying space.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A Torsion-Free Group Algebra with Zero Divisors",
"titleZh": "一个含零因子的无挠群代数",
"details": {
"overview": "该稿件声称否证了Kaplansky零因子猜想，构造了一个有限表示的无挠群G，使得𝔽2[G]含有非零零因子。摘要还表示该群具有有限二维分类空间。研究对象属于群环与零因子猜想；手稿为AI产生，收录不表示已完成独立审查或同行评议，当前收录摘要未给出构造细节。",
"keyPoints": [
"构造有限表示无挠群G使𝔽2[G]有零因子",
"声称否证Kaplansky零因子猜想",
"该群具有有限二维分类空间"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "群环理论",
"interest": []
},
{
"id": "759a7c175db5963e",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Triangular minimality for planar Coulomb renormalized energy",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Triangular-minimality-for-planar-Coulomb-renormalized-energy-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Sandier–Serfaty conjecture: the triangular lattice of covolume one minimizes planar Coulomb renormalized energy over all admissible curl-free fields with a unit uniform background. Combined with Bétermin and Sandier's asymptotic formula, this also proves the Brauchart–Hardin–Saff conjecture for the linear term of optimal ordered-pair logarithmic energy on the unit two-sphere. The proof uses a direct Voronoi-cell comparison with rigorous interval arithmetic.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Triangular minimality for planar Coulomb renormalized energy",
"titleZh": "平面Coulomb重整化能量的三角极小性",
"details": {
"overview": "该稿件声称证明了Sandier–Serfaty猜想：在具有单位均匀背景的所有容许无旋场中，余体积为一的三角格点使平面Coulomb重整化能量最小。摘要表示，结合Bétermin与Sandier的渐近公式，还可证明单位二维球面上最优有序对对数能量线性项的Brauchart–Hardin–Saff猜想。证明采用直接的Voronoi胞腔比较与严格区间算术。手稿为AI产生，未经独立审查。",
"keyPoints": [
"三角格点在容许无旋场中最小化重整化能量",
"结合渐近公式推出Brauchart–Hardin–Saff猜想",
"证明方法为Voronoi胞腔比较加区间算术"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学分析",
"interest": []
},
{
"id": "72bd98309334a601",
"section": "papers",
"category": "概率与统计",
"title": "The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the height function of the square-lattice six-vertex model with weights $`a=b=1`$ and $`0\\lt c\\le2`$, in the plane state obtained from balanced tori, converges to a multiple of the Gaussian free field. For unit height jumps and Green kernel $`-(2\\pi)^{-1}\\log|x-y|`$, the squared multiplier is $`1/\\arcsin(c/2)`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)",
"titleZh": "平衡六顶点模型的高斯自由场极限与方差乘子1/arcsin(c/2)",
"details": {
"overview": "该稿件研究方格六顶点模型在权重a=b=1、0 0 and rotation $`0\\lt |\\mathfrak a|\\lt M`$, we prove that the smooth vacuum data near its complete two-ended bridge whose full maximal globally hyperbolic development admits a future $`C^0\\cap W^{1,2}_{\\mathrm{loc}}`$ extension form a meagre set in the weighted smooth topology. The extension metric is continuous and nondegenerate, and its weak connection is locally square-integrable. The neighborhood requires smallness of only the tenth weighted seminorm, while the topology tests every finite order.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime",
"titleZh": "固定Kerr时空附近具平方可积联络的通用未来不可延拓性",
"details": {
"overview": "稿件针对每个固定的旋转次极端Kerr背景（质量M>0、旋转参数满足0<|𝔞| 1, approximating Min-UnCut within factor C is NP-hard, even on simple undirected unweighted graphs.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Constant-factor hardness of Min-UnCut",
"titleZh": "Min-UnCut的常数因子硬度",
"details": {
"overview": "稿件研究Min-UnCut问题的近似硬度。作者声称对每个固定常数C>1，即使在简单无向无权图上，将Min-UnCut近似到因子C以内也是NP困难的。该结论若成立，说明该问题不存在优于某常数因子的多项式时间近似，属于组合优化与计算复杂性中的不可近似性结果；但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"研究对象为简单无向无权图上的Min-UnCut",
"作者声称对每个固定C>1，C因子近似均为NP困难",
"当前收录摘要未给出具体常数或归约细节"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "计算复杂性",
"interest": []
},
{
"id": "546543cef9c5deb2",
"section": "papers",
"category": "组合数学与图论",
"title": "Quantitative Superexponential Bounds for van der Waerden Numbers",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Quantitative-Superexponential-Bounds-for-van-der-Waerden-Numbers-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that there are absolute constants c > 0 and K0 such that $`W_r(k)\\gt k^{ck\\lfloor\\log_2 r\\rfloor}`$ for every $`k\\ge K_0`$ and r ≥ 2. Consequently $`W_r(k)^{1/k}\\to\\infty`$ for each fixed r ≥ 2, giving a quantitative positive resolution of Erdős's superexponential-growth question, including the two-color case.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Quantitative Superexponential Bounds for van der Waerden Numbers",
"titleZh": "van der Waerden数的定量超指数界",
"details": {
"overview": "稿件研究van der Waerden数W_r(k)的增长下界。作者声称存在绝对常数c>0与K₀，使得对所有k≥K₀和r≥2有W_r(k)>k^{ck⌊log₂r⌋}；由此对每个固定r≥2，W_r(k)^{1/k}趋于无穷。摘要表示这定量地正面解决了Erdős关于超指数增长的问题，包括两色情形。该结果属于Ramsey理论与组合数论，但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"作者声称W_r(k)>k^{ck⌊log₂r⌋}对k≥K₀、r≥2成立",
"由此对每个固定r≥2有W_r(k)^{1/k}→∞",
"摘要表示定量正面解决Erdős超指数增长问题，含两色情形"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "53fee2ed9501fbef",
"section": "papers",
"category": "组合数学与图论",
"title": "The weak pinned planar distance theorem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-weak-pinned-planar-distance-theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the weak pinned Erdős distinct-distance conjecture. For every fixed ε > 0, all but $`o(n)`$ points of any n-point planar set determine at least $`n^{1-\\varepsilon}`$ distinct nonzero distances.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The weak pinned planar distance theorem",
"titleZh": "弱钉扎平面距离定理",
"details": {
"overview": "稿件研究平面点集的距离计数问题，证明弱钉扎Erdős不同距离猜想。作者声称对每个固定ε>0，任意n点平面集中除o(n)个点外，其余点至少确定n^{1-ε}个不同的非零距离。该结果属于离散几何与组合几何中Erdős距离问题的弱化形式，若成立可推进对平面点集距离下界的理解；但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"研究平面n点集的弱钉扎不同距离问题",
"作者声称除o(n)个点外，其余点至少确定n^{1-ε}个非零距离",
"结论对每个固定ε>0成立"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与离散几何",
"interest": []
},
{
"id": "524a4120591aaac8",
"section": "papers",
"category": "分析与偏微分方程",
"title": "An irrational-trace counterexample to reduced Baum–Connes",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a finitely generated discrete group whose reduced group C∗-algebra contains a projection of irrational canonical trace. Its K0-class lies outside the image of the coefficient-free reduced Baum–Connes assembly map. This disproves the coefficient-free reduced Baum–Connes conjecture for countable discrete groups.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "An irrational-trace counterexample to reduced Baum–Connes",
"titleZh": "约化Baum–Connes的无理迹反例",
"details": {
"overview": "稿件构造了一个有限生成离散群，作者声称其约化群C*-代数含有一个具有无理典范迹的投影，该投影的K₀类不在无系数约化Baum–Connes装配映射的像中。摘要表示这否定了可数离散群的无系数约化Baum–Connes猜想。该结果涉及算子代数与非交换几何中的核心猜想，若成立影响深远；但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"构造有限生成离散群，其约化群C*-代数含无理典范迹投影",
"作者声称该投影K₀类不在无系数约化装配映射像中",
"摘要表示由此否定可数离散群的无系数约化Baum–Connes猜想"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "506a4785197ba715",
"section": "papers",
"category": "理论计算机科学",
"title": "A Direct Proof of Optimal Max-Cut Hardness",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Direct-Proof-of-Optimal-Max-Cut-Hardness-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that approximating Max-Cut on simple unweighted graphs within any fixed factor greater than the Goemans–Williamson constant is NP-hard.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A Direct Proof of Optimal Max-Cut Hardness",
"titleZh": "最优Max-Cut硬度的直接证明",
"details": {
"overview": "稿件研究简单无权图上Max-Cut的近似硬度。作者声称证明：将Max-Cut近似到任何大于Goemans–Williamson常数的固定因子都是NP困难的。该结论若成立，将以直接证明方式确立Max-Cut的最优近似阈值，属于组合优化与计算复杂性中的经典问题；但作为AI产生的研究手稿，尚未经独立审查或同行评议，摘要也未给出归约或证明细节。",
"keyPoints": [
"研究对象为简单无权图上的Max-Cut近似",
"作者声称任何大于Goemans–Williamson常数的固定因子均NP困难",
"摘要称给出直接证明，未展开归约细节"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "计算复杂性",
"interest": []
},
{
"id": "4f7929b0fbc7bebb",
"section": "papers",
"category": "代数与表示论",
"title": "A universal group of type F∞",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-universal-group-of-type-F-infinity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a single group of type F∞ containing every finitely presented group. Its finitely generated subgroups, up to isomorphism, are exactly the finitely generated recursively presented groups. This answers the F∞ form of the higher-dimensional Higman embedding question.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A universal group of type F∞",
"titleZh": "一个通用的F∞型群",
"details": {
"overview": "稿件构造了一个单一的F∞型群，作者声称它包含每个有限呈现群，且其有限生成子群在同构意义下恰好是所有有限生成递归呈现群。摘要表示这回答了Higman嵌入问题的F∞形式。该结果属于几何群论与可计算群论，若成立将统一嵌入有限呈现群与递归呈现群的框架；但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"构造单一F∞型群，作者声称包含每个有限呈现群",
"其有限生成子群同构类恰为有限生成递归呈现群",
"摘要表示回答Higman嵌入问题的F∞形式"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何群论",
"interest": []
},
{
"id": "4f69beed5891d6d9",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Unitarizability implies amenability for discrete groups",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that a discrete group is amenable if and only if every uniformly bounded representation on a complex Hilbert space is similar to a unitary representation. This resolves Dixmier's unitarizability problem affirmatively for discrete groups.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Unitarizability implies amenability for discrete groups",
"titleZh": "离散群的可单位化蕴含顺从性",
"details": {
"overview": "稿件研究离散群上一致有界表示与酉表示的关系。作者声称证明：离散群顺从当且仅当其复Hilbert空间上每个一致有界表示都相似于酉表示。摘要表示这正面解决了离散群的Dixmier可单位化问题。该结果连接算子代数中的顺从性与表示论，若成立意义重大；但作为AI产生的研究手稿，尚未经独立审查或同行评议。",
"keyPoints": [
"研究离散群一致有界表示与酉表示的相似性",
"作者声称顺从当且仅当每个一致有界表示相似于酉表示",
"摘要表示正面解决离散群的Dixmier可单位化问题"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数与群论",
"interest": []
},
{
"id": "49d2fcb753d9e5a8",
"section": "papers",
"category": "理论计算机科学",
"title": "Exact derandomization of logarithmic space: L = RL = BPL",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove $`\\mathsf L=\\mathsf{RL}=\\mathsf{BPL}`$, resolving the derandomization problem for polynomial-time randomized logarithmic space.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Exact derandomization of logarithmic space: L = RL = BPL",
"titleZh": "对数空间的精确去随机化：L = RL = BPL",
"details": {
"overview": "该稿件研究多项式时间随机对数空间（RL、BPL）能否去随机化。作者声称证明了 L = RL = BPL，即随机对数空间类与确定性对数空间类相等，从而解决该去随机化问题。若成立，将说明随机性在对数空间计算中不增加能力。但该手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称证明 L = RL = BPL，解决多项式时间随机对数空间的去随机化问题。",
"结果若成立，意味着随机对数空间计算可被确定性对数空间模拟。",
"手稿为AI产生，未经独立审查或同行评议，结论需谨慎看待。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "计算复杂性理论",
"interest": []
},
{
"id": "493fe587c4080843",
"section": "papers",
"category": "代数几何",
"title": "A surface counterexample to Shafarevich holomorphic convexity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a smooth connected projective complex surface whose universal cover is not holomorphically convex. This disproves the Shafarevich conjecture on holomorphic convexity in complex dimension two.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A surface counterexample to Shafarevich holomorphic convexity",
"titleZh": "Shafarevich全纯凸性的一则曲面反例",
"details": {
"overview": "该稿件研究复曲面万有覆叠的全纯凸性。作者声称构造了一个光滑连通射影复曲面，其万有覆叠不是全纯凸的，从而在复维数二否定Shafarevich关于全纯凸性的猜想。该结果若成立，将给出该猜想的反例。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待独立验证。",
"keyPoints": [
"作者声称构造光滑连通射影复曲面，其万有覆叠非全纯凸。",
"该构造在复维数二否定Shafarevich全纯凸性猜想。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "复几何",
"interest": []
},
{
"id": "46b17b220ed36e17",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Koebe's Circle-Domain Conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Koebes-Circle-Domain-Conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every domain in the Riemann sphere is conformally equivalent to a circle domain, resolving Koebe's circle-domain conjecture positively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Koebe's Circle-Domain Conjecture",
"titleZh": "Koebe圆域猜想",
"details": {
"overview": "该稿件研究黎曼球面上区域的全纯等价分类。作者声称证明了黎曼球面上每个区域都共形等价于一个圆域，从而正面解决Koebe圆域猜想。该猜想涉及区域边界由圆或点组成的标准形式。若成立，将为单复变函数论中的共形分类提供统一结论。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称证明黎曼球面上每个区域共形等价于一个圆域。",
"该结果正面解决Koebe圆域猜想。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "复分析",
"interest": []
},
{
"id": "43bb16a115f6a43a",
"section": "papers",
"category": "概率与统计",
"title": "Talagrand’s discrete-convexity conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Talagrands-discrete-convexity-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Talagrand's discrete-convexity conjecture. There is a universal integer k such that, whenever an arbitrary family has Bernoulli product measure at least $`1-1/k`$, the sets not contained in a union of k members admit a cover of total cost at most 1/2 at the same density.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Talagrand’s discrete-convexity conjecture",
"titleZh": "Talagrand离散凸性猜想",
"details": {
"overview": "该稿件研究Talagrand提出的离散凸性猜想。作者声称证明该猜想：存在通用整数k，使得当任意族在Bernoulli乘积测度下密度至少为1−1/k时，不被k个成员之并包含的集合可在相同密度下以总成本不超过1/2的方式被覆盖。该结果涉及离散凸性与覆盖成本的关系。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称证明Talagrand离散凸性猜想。",
"结论给出通用整数k，并涉及相同密度下总成本不超过1/2的覆盖。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与组合数学",
"interest": []
},
{
"id": "4299d35895804670",
"section": "papers",
"category": "组合数学与图论",
"title": "A polynomial-time construction of strong thin trees",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-polynomial-time-construction-of-strong-thin-trees-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We give a deterministic polynomial-time construction of strong thin trees. Given a finite k-edge-connected loopless multigraph on at least one vertex, the algorithm constructs a spanning tree meeting every cut in at most a $`C/k`$ fraction of its edges, for a universal constant C. The running time is polynomial in the binary input length, including when parallel-edge multiplicities are encoded in binary.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A polynomial-time construction of strong thin trees",
"titleZh": "强细树的多项式时间构造",
"details": {
"overview": "该稿件研究有限多重图中强细树的构造算法。作者声称给出强细树的确定性多项式时间构造：对至少一个顶点上的有限k边连通无环多重图，算法构造一棵生成树，使每个割至多包含其C/k比例的边，C为通用常数；运行时间对二进制输入长度（含平行边重数用二进制编码）为多项式。该结果若成立，将把强细树的存在性推进为有效构造。但手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"作者声称给出强细树的确定性多项式时间构造算法。",
"生成树在每个割中至多占C/k比例的边，C为通用常数。",
"运行时间对二进制输入长度为多项式，含平行边重数二进制编码。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算法与组合优化",
"interest": []
},
{
"id": "41ef6c2ebb5dcc24",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Power-law violations of Yau's nodal upper bound",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a smooth Riemannian metric on $`S^4\\times S^1`$ and a sequence of real Laplace eigenfunctions whose nodal four-volume grows faster than $`\\lambda^{1/2+\\epsilon_0}`$ for one fixed $`\\epsilon_0\\gt 0`$. This disproves the smooth upper-bound assertion in Yau's nodal-set conjecture and the proposed bound with an arbitrarily small positive power loss.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Power-law violations of Yau's nodal upper bound",
"titleZh": "Yau节点上界的多项式律违反",
"details": {
"overview": "该稿件研究黎曼流形上Laplace特征函数节点集体积的上界。作者声称在S^4×S^1上构造光滑黎曼度量及一列实Laplace特征函数，其节点四维体积增长快于λ^{1/2+ε0}，ε0为某固定正数。据此否定Yau节点集猜想中的光滑上界断言，以及允许任意小正幂损失的拟议上界。该结果若成立，将表明节点集体积可超出现有猜想上界。但手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"作者在S^4×S^1上构造度量与特征函数列，节点四维体积增长快于λ^{1/2+ε0}。",
"该构造否定Yau节点集猜想的光滑上界断言及带小幂损失的拟议上界。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何分析",
"interest": []
},
{
"id": "4149b3aa386e4a3f",
"section": "news",
"category": "行业新闻",
"title": "OpenAI extends cyber access to Ukraine for civilian defense",
"summary": "该消息称，OpenAI 将其 Daybreak 项目的访问权限扩展至乌克兰政府，用于支持民用基础设施的网络防御。",
"url": "https://openai.com/index/openai-extends-cyber-access-to-ukraine-for-civilian-defense",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T13:00:00+00:00",
"titleEn": "OpenAI extends cyber access to Ukraine for civilian defense",
"titleZh": "OpenAI 将网络访问权限扩展至乌克兰用于民用防御",
"details": {
"overview": "该消息称，OpenAI 将其 Daybreak 项目的访问权限扩展至乌克兰政府，用于支持民用基础设施的网络防御。原文仅说明这一扩展的对象与用途，未披露具体范围、期限或技术细节，相关限制需以原始发布为准。",
"keyPoints": [
"OpenAI 将 Daybreak 项目访问权限扩展给乌克兰政府",
"用途为支持民用基础设施的网络防御",
"原文未说明具体范围与限制细节"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "3f53670bf1a271ab",
"section": "papers",
"category": "几何与拓扑",
"title": "Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Generalized-Cartan-Hadamard-isoperimetry-and-Euclidean-equality-rigidity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the generalized Cartan–Hadamard isoperimetric conjecture in every dimension. In a complete simply connected smooth manifold with sectional curvature at most κ ≤ 0, every finite-volume set of finite ambient perimeter has perimeter at least that of the equal-volume ball in curvature κ. For bounded positive-volume sets, equality in the Euclidean comparison holds precisely when the set agrees up to null sets with an open region isometric, with its induced metric, to a round Euclidean ball.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity",
"titleZh": "广义Cartan–Hadamard等周不等式与欧氏等号刚性",
"details": {
"overview": "该稿件研究截面曲率非正完备单连通流形中的等周不等式。作者声称在所有维数解决广义Cartan–Hadamard等周猜想：曲率至多κ≤0时，每个有限体积、有限周边长的集合，其周长至少不小于曲率κ下同体积球的周长；对有界正体积集合，欧氏比较中的等号成立当且仅当该集合（至零测集）与一个欧氏球等距。该结果给出等周比较及刚性刻画。但手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"作者声称在所有维数解决广义Cartan–Hadamard等周猜想。",
"曲率≤0时集合周长不小于同体积模型球周长。",
"欧氏比较等号成立当且仅当集合与欧氏球等距。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "黎曼几何",
"interest": []
},
{
"id": "3f4e5b8b52f1f08c",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Smooth isometric immersions of closed surfaces into Euclidean four-space",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every closed smooth Riemannian surface admits a smooth isometric immersion into Euclidean four-space, without an orientability assumption. This resolves the closed-surface form of the classical four-dimensional isometric-immersion problem.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Smooth isometric immersions of closed surfaces into Euclidean four-space",
"titleZh": "闭曲面到欧氏四维空间的光滑等距浸入",
"details": {
"overview": "该稿件研究闭曲面到欧氏四维空间的等距浸入问题。作者声称每个闭光滑黎曼曲面都可光滑等距浸入欧氏四维空间，且不假设可定向性，从而解决经典四维等距浸入问题的闭曲面情形。该结果若成立，将把Nash型嵌入理论中的维数问题在闭曲面情形下推进到四维。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称每个闭光滑黎曼曲面均可光滑等距浸入欧氏四维空间。",
"结论不要求曲面可定向，解决闭曲面形式的四维等距浸入问题。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "微分几何",
"interest": []
},
{
"id": "3ea6ec430c8603fc",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Almost-everywhere Fourier convergence in L log L",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that the ordinary symmetric Fourier partial sums of every complex-valued function in $`L\\log L`$ on the circle converge almost everywhere to the function along the full sequence. This establishes the classical $`L\\log L`$ sufficiency conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Almost-everywhere Fourier convergence in L log L",
"titleZh": "L log L中几乎处处Fourier收敛",
"details": {
"overview": "该稿件研究圆周上Fourier部分和的几乎处处收敛性。作者声称证明：圆周上每个L log L中的复值函数，其通常对称Fourier部分和沿完整序列几乎处处收敛于该函数，从而建立经典的L log L充分性猜想。该结果若成立，将给出Fourier级数几乎处处收敛的一个临界函数空间结论。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称证明L log L中函数的对称Fourier部分和几乎处处收敛。",
"该结果建立经典的L log L充分性猜想。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "调和分析",
"interest": []
},
{
"id": "3c9d4fef82f56381",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Nontrivial Markov Type Forces Superreflexivity",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every real Banach space with Markov type p > 1 is superreflexive. Together with the known converse, this characterizes superreflexivity by nontrivial Markov type. This answers Naor's question: every real Banach space with nontrivial Markov type admits an equivalent uniformly smooth norm.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Nontrivial Markov Type Forces Superreflexivity",
"titleZh": "非平凡Markov型蕴含超自反性",
"details": {
"overview": "该稿件研究Banach空间的Markov型与超自反性之间的关系。作者声称证明每个具有Markov型p>1的实Banach空间都是超自反的；结合已知逆命题，可用非平凡Markov型刻画超自反性。作者还称这回答了Naor的问题：每个具有非平凡Markov型的实Banach空间都容许等价的一致光滑范数。该结果若成立，将连接度量嵌入性质与Banach空间几何。但手稿为AI产生，未经独立审查或同行评议。",
"keyPoints": [
"作者声称Markov型p>1的实Banach空间均为超自反。",
"结合已知逆命题，以非平凡Markov型刻画超自反性。",
"作者称由此回答Naor关于等价一致光滑范数的问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "泛函分析",
"interest": []
},
{
"id": "3c2b0b0622e98756",
"section": "papers",
"category": "几何与拓扑",
"title": "Symplectic Ball Packings in Higher Dimensions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Symplectic-Ball-Packings-in-Higher-Dimensions-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that, for all integers n ≥ 3 and k ≥ 1 and all positive real capacities $`R_1,\\ldots,R_k`$, the closed standard symplectic $`2n`$-balls of these capacities embed disjointly into the interior of a ball of capacity R > 0 if and only if\n\n$`\\displaystyle \\sum_{i=1}^k R_i^n\\lt R^n, \\qquad R_i+R_j\\lt R\\quad(i\\ne j).`$\n\nCapacity is π times the squared Euclidean radius, and each embedding is defined on a neighborhood of its closed source ball. This proves Siegel and Yao's Conjecture A.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Symplectic Ball Packings in Higher Dimensions",
"titleZh": "高维辛球填充",
"details": {
"overview": "该稿件研究高维标准辛球的不相交嵌入问题。作者声称对任意整数n≥3、k≥1及正实数容量R_1,…,R_k，闭标准辛2n球可不相交嵌入容量R的球内部，当且仅当ΣR_i^n0}。该结果若成立，将统一自由群因子理论中的核心分类问题。但手稿为AI产生，收录不表示已完成独立审查或同行评议，结论尚待验证。",
"keyPoints": [
"作者声称L(F_2)与L(F_3)作为迹von Neumann代数同构。",
"作者称由此所有插值自由群因子同构，基本群为R_{>0}。",
"手稿为AI产生，未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "3a3d0b556bd855ba",
"section": "papers",
"category": "组合数学与图论",
"title": "The strong thin tree conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-strong-thin-tree-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every finite loopless k-edge-connected multigraph on at least two vertices, with k ≥ 1, has a spanning tree meeting each cut in at most $`C/k`$ times the size of the cut, where C is a universal constant. This resolves the strong thin tree conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The strong thin tree conjecture",
"titleZh": "强细树猜想",
"details": {
"overview": "稿件提出证明强细树猜想：每个至少两个顶点的有限无环k边连通多重图（k≥1）都存在一棵生成树，使得该树与任一割的交集大小不超过该割大小的C/k倍，其中C为通用常数。摘要表示这一结果解决了强细树猜想。该猜想属于图论中生成树与割结构关系的研究，若成立将深化对边连通图稀疏子图性质的理解。",
"keyPoints": [
"研究对象为有限无环k边连通多重图，k≥1且顶点数至少为二。",
"作者声称存在生成树，其与每个割的交集不超过割大小的C/k倍。",
"摘要表示该结果解决了强细树猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "图论",
"interest": []
},
{
"id": "38ceb09a26420cc3",
"section": "papers",
"category": "概率与统计",
"title": "The Mézard–Parisi formula for diluted spin glasses",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Mézard–Parisi hierarchical cavity formula for diluted even-arity Ising models in the Panchenko–Talagrand class. This resolves the variational equality conjecture for that class: the limiting pressure equals the infimum of the trial functional over all finite hierarchy depths and trial laws. Only first moments of the interaction and external field are required.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Mézard–Parisi formula for diluted spin glasses",
"titleZh": "稀释自旋玻璃的Mézard–Parisi公式",
"details": {
"overview": "稿件针对Panchenko–Talagrand类中的稀释偶数元Ising模型，证明Mézard–Parisi分层空腔公式。摘要表示这解决了该类的变分等式猜想：极限压强等于在所有有限层级深度和试验律上试验泛函的下确界，且仅需相互作用与外场的一阶矩。该结果若成立，将为稀释自旋玻璃的平均场理论提供严格数学基础。",
"keyPoints": [
"研究对象是Panchenko–Talagrand类中的稀释偶数元Ising模型。",
"作者声称证明Mézard–Parisi分层空腔公式并解决变分等式猜想。",
"结果仅要求相互作用和外场的一阶矩。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与数学物理",
"interest": []
},
{
"id": "389ce694d9d7442a",
"section": "papers",
"category": "组合数学与图论",
"title": "A linear list-coloring bound in terms of the Hadwiger number",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every finite nonempty graph G satisfies $`\\chi_{\\mathrm{list}}(G)\\le C h(G)`$ for an absolute integer C, where $`h(G)`$ is the largest order of a clique minor. This resolves the Linear List Hadwiger conjecture affirmatively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A linear list-coloring bound in terms of the Hadwiger number",
"titleZh": "基于Hadwiger数的线性列表染色界",
"details": {
"overview": "稿件证明每个有限非空图G满足χ_list(G) ≤ C h(G)，其中h(G)是最大团子式阶数，C为绝对整数常数。摘要表示这肯定地解决了线性列表Hadwiger猜想。该猜想将列表染色数与团子式结构联系起来，若成立将推进图染色理论中Hadwiger型问题的定量研究。",
"keyPoints": [
"研究对象为有限非空图的列表染色数χ_list(G)与最大团子式阶数h(G)。",
"作者声称存在绝对常数C使χ_list(G) ≤ C h(G)对所有图成立。",
"摘要表示该结果肯定地解决了线性列表Hadwiger猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "图论",
"interest": []
},
{
"id": "388188c7618b55cd",
"section": "papers",
"category": "代数与表示论",
"title": "A counterexample to Tachikawa's second conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove Tachikawa's second conjecture by constructing a finite-dimensional symmetric algebra over $`k=\\mathbb F_2(q,H_1,H_2)`$ with a finite-dimensional nonprojective module whose self-extension groups vanish in every positive degree. The associated endomorphism algebra also gives counterexamples to the classical, generalized, and strong Nakayama conjectures, the Auslander–Gorenstein conjecture, and the Wakamatsu tilting conjecture. These conclusions persist after every extension of k.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A counterexample to Tachikawa's second conjecture",
"titleZh": "Tachikawa第二猜想的反例",
"details": {
"overview": "稿件通过构造k=F_2(q,H_1,H_2)上的有限维对称代数，给出一个有限维非投射模，其各正次自扩张群均为零，从而否定Tachikawa第二猜想。摘要还称相关自同态代数同时构成经典、广义和强Nakayama猜想、Auslander–Gorenstein猜想及Wakamatsu倾斜猜想的反例，且这些结论在k的任意扩域后仍成立。该结果若成立将对代数表示论中多个长期猜想产生冲击。",
"keyPoints": [
"构造有限维对称代数上的非投射模，其所有正次自扩张群为零。",
"作者声称该构造否定Tachikawa第二猜想。",
"摘要表示同一构造还给出多个Nakayama型及倾斜猜想的反例。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数表示论",
"interest": []
},
{
"id": "38254ac4dbc7c2bc",
"section": "papers",
"category": "代数几何",
"title": "Integrability of split tangent bundles on rationally connected manifolds",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that both summands of every specified holomorphic splitting of the tangent bundle of a smooth rationally connected projective complex manifold into two positive-rank subbundles are integrable. This proves Höring's conjecture on rationally connected projective manifolds. Höring's product theorem then gives a product decomposition compatible with the specified splitting.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Integrability of split tangent bundles on rationally connected manifolds",
"titleZh": "有理连通流形上分裂切丛的可积性",
"details": {
"overview": "稿件证明：光滑有理连通射影复流形的切丛若按指定方式全纯分裂为两个正秩子丛，则两个子丛均可积。摘要表示这证明了Höring关于有理连通射影流形的猜想，并结合Höring乘积定理得到与该分裂相容的乘积分解。该结果若成立将深化对有理连通流形切丛结构与乘积分解之间关系的理解。",
"keyPoints": [
"研究对象为光滑有理连通射影复流形切丛的全纯分裂。",
"作者声称分裂所得两个正秩子丛均可积，证明Höring猜想。",
"结合Höring乘积定理可得到与分裂相容的乘积分解。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "36a9fde4b4829ea2",
"section": "papers",
"category": "概率与统计",
"title": "Square-lattice FK interfaces and nested loops for 1 <= q < 4",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed $`1\\le q\\lt 4`$, critical square-lattice random-cluster Dobrushin interfaces converge as ordered curves to chordal $`\\mathop{\\mathrm{SLE}}\\nolimits _{\\kappa(q)}`$, where $`\\kappa(q)=4\\pi/\\arccos(-\\sqrt q/2)`$, confirming the Rohde–Schramm prediction in this parameter range. This holds in every bounded Jordan domain under uniform marked boundary approximation. The complete nested plane loop collections converge to whole-plane $`\\mathop{\\mathrm{CLE}}\\nolimits _{\\kappa(q)}`$ in a spherical matching topology retaining multiplicities and traversals. At q = 1 we obtain Cardy's formula for square-lattice bond percolation with free boundary edges.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Square-lattice FK interfaces and nested loops for 1 <= q < 4",
"titleZh": "1 ≤ q < 4 时方格FK界面与嵌套环",
"details": {
"overview": "稿件研究临界方格随机簇模型的Dobrushin界面，对每个固定1≤q<4，证明其在有界Jordan域及一致标记边界逼近下按有序曲线收敛到弦形SLE_{κ(q)}，其中κ(q)=4π/arccos(-√q/2)，从而在该参数范围确认Rohde–Schramm预测。摘要还称完整嵌套平面环集合在保留重数和遍历的球面匹配拓扑下收敛到全平面CLE_{κ(q)}，并在q=1时得到自由边界边键渗流的Cardy公式。",
"keyPoints": [
"对每个固定1≤q<4，临界方格随机簇Dobrushin界面收敛到弦形SLE_{κ(q)}。",
"κ(q)=4π/arccos(-√q/2)，摘要称确认了Rohde–Schramm预测。",
"嵌套环集合收敛到全平面CLE_{κ(q)}，q=1时得到Cardy公式。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与统计物理",
"interest": []
},
{
"id": "34d49af720b7e961",
"section": "papers",
"category": "分析与偏微分方程",
"title": "The Kakeya maximal conjecture in three dimensions",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Kakeya maximal conjecture in three dimensions. For every ε > 0, the maximal average over unit tubes of radius δ maps $`L^3(\\mathbb R^3)`$ to $`L^3(S^2)`$ with norm at most $`C_\\varepsilon\\delta^{-\\varepsilon}`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Kakeya maximal conjecture in three dimensions",
"titleZh": "三维Kakeya极大猜想",
"details": {
"overview": "稿件证明三维Kakeya极大猜想：对每个ε>0，半径δ的单位管上的极大平均算子将L^3(R^3)映射到L^3(S^2)，其范数至多为C_ε δ^{-ε}。摘要表示这解决了三维Kakeya极大猜想。该猜想是调和分析中Kakeya问题的核心形式之一，若成立将对限制型估计和几何测度论产生重要影响。",
"keyPoints": [
"研究对象是三维空间中单位管上的Kakeya极大平均算子。",
"作者声称该算子从L^3(R^3)到L^3(S^2)的范数至多为C_ε δ^{-ε}。",
"摘要表示这证明了三维Kakeya极大猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "调和分析",
"interest": []
},
{
"id": "34ca6adb7f07ea43",
"section": "papers",
"category": "几何与拓扑",
"title": "A counterexample to the coarse Novikov conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-coarse-Novikov-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove the coarse Novikov conjecture: ordinary coarse assembly need not be rationally injective for uniformly discrete spaces of bounded geometry. We construct a coarse disjoint union of finite graphs of uniformly bounded degree and an infinite-order class in its degree-one coarse K-homology whose image under ordinary coarse assembly in the K-theory of the reduced, locally compact Roe algebra vanishes.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A counterexample to the coarse Novikov conjecture",
"titleZh": "粗Novikov猜想的反例",
"details": {
"overview": "稿件否定粗Novikov猜想：摘要称对一致离散的有界几何空间，普通粗装配不必有理单射。作者构造有限图的粗不交并（度一致有界），并在其一次粗K同调中给出一个无限阶类，该类的像在约化局部紧Roe代数的K理论中经普通粗装配后为零。该结果若成立将对粗几何与指标理论中的Novikov型问题产生重大影响。",
"keyPoints": [
"构造度一致有界的有限图粗不交并作为反例空间。",
"给出一次粗K同调中的无限阶类，其粗装配像为零。",
"作者声称这否定粗Novikov猜想中有理单射性的一般陈述。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "粗几何与指标理论",
"interest": []
},
{
"id": "342ff5cfd116d294",
"section": "papers",
"category": "几何与拓扑",
"title": "Three fixed points on the symplectic quadric threefold",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We construct a smooth Hamiltonian diffeomorphism of the complex quadric threefold with exactly three fixed points, at least one of which is degenerate. The critical number and the unit-inclusive rational cup length of this manifold are both four. Thus the example disproves the unrestricted critical-number and rational cup-length forms of the Arnold conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Three fixed points on the symplectic quadric threefold",
"titleZh": "辛四维二次超曲面上的三个不动点",
"details": {
"overview": "稿件在复四维二次超曲面上构造一个光滑哈密顿微分同胚，恰有三个不动点，且至少一个退化。摘要指出该流形的临界数与含单位有理杯长均为四，因此该例子否定Arnold猜想中无限制的临界数形式和有理杯长形式。该结果若成立将揭示Arnold猜想在一般辛流形上的适用边界。",
"keyPoints": [
"在复四维二次超曲面上构造恰有三个不动点的光滑哈密顿微分同胚。",
"至少一个不动点是退化的，且临界数与有理杯长均为四。",
"作者声称该例子否定Arnold猜想的无限制临界数和有理杯长形式。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "辛几何与哈密顿动力学",
"interest": []
},
{
"id": "3402ec396ec2da9f",
"section": "papers",
"category": "代数与表示论",
"title": "Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Eisenbud–Green–Harris conjecture over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. Thus every homogeneous ideal containing such a sequence has the Hilbert function of a monomial ideal containing the corresponding pure powers.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture",
"titleZh": "交换除系数形式与Artin型Eisenbud–Green–Harris猜想",
"details": {
"overview": "稿件证明：在任意特征零域上，对任意正长度且次数至少为二的齐次正则序列，Eisenbud–Green–Harris猜想成立。摘要表示由此每个包含此类序列的齐次理想，其Hilbert函数与某个包含相应纯幂单项式理想的Hilbert函数相同。该结果若成立将推进交换代数中理想Hilbert函数与单项式理想比较的研究。",
"keyPoints": [
"在特征零域上对任意正长度、次数至少二的齐次正则序列证明EGH猜想。",
"结论是含该序列的齐次理想具有与含对应纯幂的单项式理想相同的Hilbert函数。",
"摘要称该结果覆盖任意正长度的齐次正则序列。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "交换代数",
"interest": []
},
{
"id": "31a17bbcfc8d57ea",
"section": "papers",
"category": "组合数学与图论",
"title": "Integral and fractional expectation thresholds are equivalent",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Integral-and-fractional-expectation-thresholds-are-equivalent-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Talagrand's conjecture that integral and fractional expectation thresholds are within a universal constant factor, with the same covering budget.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Integral and fractional expectation thresholds are equivalent",
"titleZh": "整期望阈值与分数期望阈值等价",
"details": {
"overview": "稿件证明Talagrand的猜想：整期望阈值与分数期望阈值之间相差一个通用常数因子，且具有相同的覆盖预算。摘要表示这解决了该猜想。该结果若成立将统一组合学中两类期望阈值概念，对随机结构阈值分析具有基础意义。",
"keyPoints": [
"研究对象是整期望阈值与分数期望阈值的关系。",
"作者声称两者在相同覆盖预算下相差一个通用常数因子。",
"摘要表示这证明了Talagrand的猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学",
"interest": []
},
{
"id": "30c52194499122f2",
"section": "papers",
"category": "代数几何",
"title": "Every complex K3 surface is Oka",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every complex K3 surface X is Oka, resolving the K3 Oka conjecture. Equivalently, for every m ≥ 1, every holomorphic map to X from a neighborhood of a compact convex set in ℂm can be approximated uniformly on that set by entire maps $`\\mathbb C^m\\to X`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Every complex K3 surface is Oka",
"titleZh": "每个复K3曲面都是Oka的",
"details": {
"overview": "稿件证明每个复K3曲面X都是Oka的，从而解决K3 Oka猜想。等价地，对每个m≥1，从ℂ^m中紧凸集邻域到X的每个全纯映射，都可在该集合上被整映射ℂ^m→X一致逼近。摘要表示这解决了K3 Oka猜想。该结果若成立将把Oka理论中的逼近性质推广到K3曲面这一类重要复流形。",
"keyPoints": [
"作者声称每个复K3曲面都是Oka的，解决K3 Oka猜想。",
"等价表述为紧凸集邻域上的全纯映射可被整映射一致逼近。",
"逼近对每个m≥1及ℂ^m中紧凸集邻域成立。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "复几何",
"interest": []
},
{
"id": "304d00be11c6fc87",
"section": "papers",
"category": "概率与统计",
"title": "Buffered comparison and stopping-band resolution in critical Ising",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove pointwise comparison and finite stopping-band approximation theorems for the critical nearest-neighbor Ising model on the square lattice. Arbitrary common pinned spins are allowed in the comparison: the likelihood ratio is controlled by a zero-field FK connection probability on the graph with those vertices deleted. For an interface exploration across a band of fixed positive width, finitely many regular signed barriers approximate every good conditional target law in total variation, uniformly over bounded observables and sufficiently fine meshes.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Buffered comparison and stopping-band resolution in critical Ising",
"titleZh": "临界Ising模型中的缓冲比较与停止带分辨率",
"details": {
"overview": "稿件研究正方形格点上临界最近邻Ising模型的逐点比较与有限停止带近似定理。作者声称允许任意共同钉扎自旋，似然比由删除这些顶点后的零场FK连接概率控制；对于固定正宽度带上的界面探索，有限多个正则符号屏障在总变差意义下一致逼近每个良好条件目标律，且对 bounded observables 和足够细网格一致。该结果若成立，可为临界Ising界面的精细概率描述提供工具。",
"keyPoints": [
"允许任意共同钉扎自旋，似然比由删除顶点后的零场FK连接概率控制。",
"对固定正宽度带上的界面探索，有限正则符号屏障一致逼近良好条件目标律。",
"逼近在总变差意义下对 bounded observables 和足够细网格一致成立。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "概率论与统计物理",
"interest": []
},
{
"id": "2f641810a76fa0cd",
"section": "news",
"category": "行业新闻",
"title": "Ringg’s AI agents resolve up to 65% of customer calls with OpenAI",
"summary": "该消息称，Ringg 使用 GPT-5.6 在语音、聊天、WhatsApp 和网页等渠道运行多语言智能体，可解决最高 65% 的客户来电，且相较 GPT-4.1 成本降低 90%。",
"url": "https://openai.com/index/ringg",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T12:00:00+00:00",
"titleEn": "Ringg’s AI agents resolve up to 65% of customer calls with OpenAI",
"titleZh": "Ringg 的 AI 智能体借助 OpenAI 解决最高 65% 的客户来电",
"details": {
"overview": "该消息称，Ringg 使用 GPT-5.6 在语音、聊天、WhatsApp 和网页等渠道运行多语言智能体，可解决最高 65% 的客户来电，且相较 GPT-4.1 成本降低 90%。上述比例与成本对比均为原文表述，具体统计口径与适用范围未在材料中说明。",
"keyPoints": [
"Ringg 基于 GPT-5.6 运行多语言客服智能体",
"覆盖语音、聊天、WhatsApp 与网页渠道",
"原文称可解决最高 65% 来电，成本较 GPT-4.1 低 90%"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "2c468a27147e84e5",
"section": "news",
"category": "模型动态",
"title": "Airbnb widens access to GPT-6 Astra and OpenAI frontier models",
"summary": "该消息介绍 Airbnb 扩大对 GPT-6 Astra 及 OpenAI 前沿模型的访问，以帮助工程团队排查缺陷、设计系统并加快交付。",
"url": "https://openai.com/index/airbnb-gpt-6-astra",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T01:00:00+00:00",
"titleEn": "Airbnb widens access to GPT-6 Astra and OpenAI frontier models",
"titleZh": "Airbnb 扩大 GPT-6 Astra 与 OpenAI 前沿模型的访问范围",
"details": {
"overview": "该消息介绍 Airbnb 扩大对 GPT-6 Astra 及 OpenAI 前沿模型的访问，以帮助工程团队排查缺陷、设计系统并加快交付。当前收录材料仅给出这一用途概述，未说明接入规模、具体流程或效果数据，相关范围与限制需以原始发布为准。",
"keyPoints": [
"Airbnb 扩大对 GPT-6 Astra 等 OpenAI 前沿模型的访问",
"目标用途包括排查缺陷、设计系统与加快交付",
"当前收录材料未提供接入规模或效果数据"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "2c1ad30369e20040",
"section": "papers",
"category": "理论计算机科学",
"title": "The Unique Games Theorem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Unique Games Conjecture. For every fixed $`\\varepsilon,\\delta\\in(0,1/2)`$, we give a deterministic polynomial-time reduction from 3SAT to Unique Games over a fixed finite alphabet, with completeness at least $`1-\\varepsilon`$ and soundness at most δ.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Unique Games Theorem",
"titleZh": "唯一游戏定理",
"details": {
"overview": "稿件声称证明唯一游戏猜想。摘要表示：对每个固定ε,δ∈(0,1/2)，给出从3SAT到固定有限字母表上唯一游戏的确定性多项式时间归约，完备性至少1-ε，可靠性至多δ。若成立，这将确立唯一游戏猜想，并对近似算法复杂性理论产生重大影响。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"声称对每个固定ε,δ∈(0,1/2)构造从3SAT到唯一游戏的确定性多项式时间归约。",
"归约的完备性至少1-ε，可靠性至多δ，字母表固定有限。",
"若成立则证明唯一游戏猜想，但稿件未经同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "理论计算机科学与组合优化",
"interest": []
},
{
"id": "2a9d715a64630ae1",
"section": "news",
"category": "模型动态",
"title": "How invideo improves color grading 3x with GPT‑6 Astra",
"summary": "该消息称，invideo 使用 GPT-6 Astra 更精确地规划剪辑，将色彩校正与调色效率提升三倍，并在一天内产出 50 个自定义效果。",
"url": "https://openai.com/index/invideo-builds-with-gpt-6-astra",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T12:00:00+00:00",
"titleEn": "How invideo improves color grading 3x with GPT‑6 Astra",
"titleZh": "invideo 借助 GPT-6 Astra 将调色效率提升三倍",
"details": {
"overview": "该消息称，invideo 使用 GPT-6 Astra 更精确地规划剪辑，将色彩校正与调色效率提升三倍，并在一天内产出 50 个自定义效果。当前收录材料仅给出这些结果性表述，未说明测试条件、对比基准或统计方法，相关结论需以原始发布为准。",
"keyPoints": [
"invideo 使用 GPT-6 Astra 更精确地规划剪辑",
"原文称色彩校正与调色效率提升三倍",
"原文称一天内可产出 50 个自定义效果"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "2648e471f764c47b",
"section": "papers",
"category": "代数与表示论",
"title": "Simple F∞ overgroups of groups with decidable word problem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Simple-F-infinity-overgroups-of-groups-with-decidable-word-problem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "Every finitely generated group with decidable word problem embeds in a simple group of type F∞. This resolves the higher-finiteness strengthening of the Boone–Higman conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Simple F∞ overgroups of groups with decidable word problem",
"titleZh": "具有可判定字问题的群的简单F∞超群",
"details": {
"overview": "稿件声称证明每个有限生成且字问题可判定的群都可嵌入一个F∞型简单群，从而解决Boone–Higman猜想的高阶有限性加强版本。当前收录摘要未给出构造细节或证明思路。若成立，该结果将把可判定字问题与高阶有限性性质联系起来，对几何群论和算法群论有潜在意义。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"声称每个有限生成且字问题可判定的群嵌入一个简单群。",
"嵌入目标群具有F∞型，即高阶有限性性质。",
"作者称这解决了Boone–Higman猜想的高阶有限性加强版。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "群论",
"interest": []
},
{
"id": "1f781105056e7e06",
"section": "chatgpt",
"category": "功能更新",
"title": "ChatGPT for iOS 1.2026.258",
"summary": "这是 ChatGPT iOS 客户端 1.2026.258 版本的更新说明，属于功能更新类发布记录。",
"url": "https://learn.chatgpt.com/docs/changelog",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "ChatGPT 与 Codex 官方变更日志",
"titleEn": "ChatGPT for iOS 1.2026.258",
"titleZh": "ChatGPT iOS 版 1.2026.258 更新",
"details": {
"overview": "这是 ChatGPT iOS 客户端 1.2026.258 版本的更新说明，属于功能更新类发布记录。原文列出新功能与改进修复两部分：重新设计的主屏幕、iPad 横屏分屏视图、嵌套 Git 仓库变更浏览，以及侧边聊天携带附件与选中文本、排队提示导致的空白回复修复、任务保留所选电脑并识别项目检出与工作树、文件链接与错误提示优化、相机和相册添加照片动画更流畅、设备时钟错误导致的配对失败及 Mac/Linux SSH 连接问题修复。原文未说明具体推出范围和限制。",
"keyPoints": [
"重新设计主屏幕，iPad 横屏新增分屏视图，可在任务旁显示任务列表。",
"侧边聊天可携带附件、选中文本和评审评论，并修复排队提示导致的空白回复。",
"修复设备时钟错误引起的配对失败，以及 Mac 和 Linux 上的 SSH 连接问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "1ddba19c70b74354",
"section": "papers",
"category": "数论与算术几何",
"title": "The Margulis–Platonov conjecture over number fields",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Margulis-Platonov-conjecture-over-number-fields-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the Margulis–Platonov conjecture over number fields. For an absolutely almost simple simply connected group, every noncentral abstract normal subgroup of its rational points is the inverse image of an open normal subgroup of the product of its anisotropic nonarchimedean local groups.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Margulis–Platonov conjecture over number fields",
"titleZh": "数域上的Margulis–Platonov猜想",
"details": {
"overview": "稿件声称证明数域上的Margulis–Platonov猜想。摘要表示：对于绝对几乎单且单连通的群，其有理点中的每个非中心抽象正规子群都是某个开正规子群的原像，该开正规子群位于其各向异性非阿基米德局部群乘积中。该结果若成立，将深化对算术群正规子群结构的理解。手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"声称对绝对几乎单单连通群证明数域上的Margulis–Platonov猜想。",
"结论刻画有理点中非中心抽象正规子群为开正规子群的原像。",
"开正规子群位于各向异性非阿基米德局部群乘积中。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数论与算术几何",
"interest": []
},
{
"id": "1d644386ea9d4cfa",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove global existence and uniqueness for arbitrary smooth admissible initial data in the three-dimensional, one-species relativistic Vlasov–Maxwell system. The particle density is initially compactly supported, and the electromagnetic fields have finite energy and bounded derivatives of all orders. The solution remains smooth on every finite time interval. This resolves the large-data global classical regularity problem for this model, without size or symmetry restrictions on the data.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system",
"titleZh": "三维相对论Vlasov–Maxwell系统的全局经典解",
"details": {
"overview": "稿件研究三维单 species 相对论Vlasov–Maxwell系统，声称对任意光滑容许初始数据证明全局存在唯一性。初始粒子密度紧支撑，电磁场有限能量且各阶导数有界；解在每个有限时间区间保持光滑。作者称这解决了该模型的大数据全局经典正则性问题，且无需对数据加尺寸或对称性限制。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对三维单species相对论Vlasov–Maxwell系统声称全局存在唯一光滑解。",
"初始数据为任意光滑容许数据，粒子密度紧支撑，场有限能量且导数有界。",
"作者称解决大数据全局经典正则性问题，无需尺寸或对称性限制。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "偏微分方程与数学物理",
"interest": []
},
{
"id": "1d0f41cd15f55614",
"section": "papers",
"category": "数学物理与量子信息",
"title": "Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For each fixed positive disorder strength, we prove that the nearest-neighbor Anderson operator on the square lattice with independent uniform site potentials almost surely has pure-point spectral type throughout its spectrum. This resolves the pure-point assertion of the two-dimensional Anderson localization conjecture for the uniform single-site law.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder",
"titleZh": "二维Anderson模型在任意正无序下的纯点谱",
"details": {
"overview": "稿件研究正方形格点上带独立均匀格点势的最近邻Anderson算子。作者声称对每个固定正无序强度，该算子几乎必然在整个谱上具有纯点谱型，从而解决二维Anderson局域化猜想中关于均匀单格点分布的纯点断言。若成立，这将为二维无序系统的谱局域化提供完整描述。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对每个固定正无序强度研究正方形格点上的最近邻Anderson算子。",
"声称几乎必然在整个谱上具有纯点谱型。",
"作者称这解决了二维Anderson局域化猜想的纯点断言（均匀单格点分布）。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理与谱理论",
"interest": []
},
{
"id": "1a7bf5ab6035cdf3",
"section": "papers",
"category": "动力系统与遍历论",
"title": "Entropy equality and local symmetry in negative curvature",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Entropy-equality-and-local-symmetry-in-negative-curvature-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, we prove that normalized Liouville measure has maximal entropy for the unit-speed geodesic flow if and only if the metric is locally symmetric. This resolves Katok's entropy rigidity conjecture positively in these dimensions, including all rank-one symmetric types at arbitrary scale.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Entropy equality and local symmetry in negative curvature",
"titleZh": "负曲率中的熵等式与局部对称性",
"details": {
"overview": "稿件研究维数至少三、截面曲率严格为负的闭连通光滑黎曼流形。作者声称证明：单位速度测地流的归一化Liouville测度具有最大熵，当且仅当度量为局部对称。这正面解决了这些维数下的Katok熵刚性猜想，并涵盖任意尺度的所有秩一对称类型。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对象为维数至少三、严格负截面曲率的闭连通黎曼流形。",
"声称归一化Liouville测度熵最大当且仅当度量局部对称。",
"作者称正面解决Katok熵刚性猜想，涵盖所有秩一对称类型。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "18afcd3597928374",
"section": "papers",
"category": "组合数学与图论",
"title": "Deterministic nonbipartite Ramanujan graphs in every fixed degree",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Deterministic-nonbipartite-Ramanujan-graphs-in-every-fixed-degree-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every fixed integer d ≥ 3, we give a deterministic algorithm that constructs a simple nonbipartite d-regular Ramanujan graph on every sufficiently large even number n of vertices. It outputs the full adjacency list in polynomially many bit operations, with an exponent that may depend on d. Every nonconstant adjacency eigenvalue lies strictly between $`-2\\sqrt{d-1}`$ and $`2\\sqrt{d-1}`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Deterministic nonbipartite Ramanujan graphs in every fixed degree",
"titleZh": "每个固定度数下的确定性非二部Ramanujan图",
"details": {
"overview": "稿件研究Ramanujan图的确定性构造。作者声称对每个固定整数d≥3，给出确定性算法，在每个足够大的偶数顶点数n上构造简单非二部d正则Ramanujan图，并以多项式位运算输出完整邻接表，指数可依赖于d；每个非平凡邻接特征值严格位于-2√(d-1)与2√(d-1)之间。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对每个固定d≥3，声称确定性构造简单非二部d正则Ramanujan图。",
"构造覆盖每个足够大的偶数顶点数n，输出完整邻接表。",
"非平凡邻接特征值严格落在±2√(d-1)之间。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "18316f3c21b6946a",
"section": "papers",
"category": "数学物理与量子信息",
"title": "Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For each fixed dimension d ≥ 3 and each fixed sufficiently small positive disorder strength, we prove that the Anderson operator on ℤd with independent uniform site potentials almost surely has purely absolutely continuous spectrum with nonzero weight on an open energy interval. The interval may depend on d but is independent of the disorder strength. This settles the purely absolutely continuous energy-range question in Simon's Problem 1 for this model.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three",
"titleZh": "维数至少三的弱无序Anderson模型的绝对连续谱",
"details": {
"overview": "稿件研究ℤd上带独立均匀格点势的Anderson算子。作者声称对每个固定维数d≥3和每个固定足够小的正无序强度，该算子几乎必然在一个开能量区间上具有非零权重的纯绝对连续谱；该区间可依赖于d但与无序强度无关。作者称这解决了Simon问题1中关于该模型的纯绝对连续能量范围问题。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对d≥3和足够小正无序强度研究ℤd上Anderson算子。",
"声称几乎必然在开能量区间上具有非零权重的纯绝对连续谱。",
"区间可依赖d但与无序强度无关，作者称解决Simon问题1的相关问题。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学物理与谱理论",
"interest": []
},
{
"id": "17a45f20b8eedff6",
"section": "papers",
"category": "代数几何",
"title": "Maximal Seshadri constants on arbitrary polarized surfaces",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that, for every smooth integral complex projective surface S and every ample line bundle L, the multipoint Seshadri constant at r very general points equals $`\\sqrt{L^2/r}`$ for every sufficiently large integer r. This resolves positively the qualitative Nagata–Biran conjecture for surfaces.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Maximal Seshadri constants on arbitrary polarized surfaces",
"titleZh": "任意极化曲面上的最大Seshadri常数",
"details": {
"overview": "稿件研究光滑整复射影曲面S和丰沛线丛L的多点Seshadri常数。作者声称对每个足够大的整数r，在r个非常一般点处的多点Seshadri常数等于√(L²/r)，从而正面解决曲面的定性Nagata–Biran猜想。该结果若成立，将给出曲面Seshadri常数在多点情形下的精确渐近值。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对象为任意光滑整复射影曲面S与丰沛线丛L。",
"声称对足够大r，r个非常一般点处多点Seshadri常数等于√(L²/r)。",
"作者称正面解决曲面的定性Nagata–Biran猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "代数几何",
"interest": []
},
{
"id": "15ee90ad025a01e6",
"section": "papers",
"category": "几何与拓扑",
"title": "Uniformization of complete Kähler manifolds with positive bisectional curvature",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every complete connected noncompact Kähler manifold with strictly positive holomorphic bisectional curvature is biholomorphic to complex Euclidean space. This resolves Yau's uniformization conjecture positively in every complex dimension.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Uniformization of complete Kähler manifolds with positive bisectional curvature",
"titleZh": "正双截曲率完备Kähler流形的单值化",
"details": {
"overview": "稿件研究完备连通非紧Kähler流形，假设其全纯双截曲率严格为正。作者声称证明该流形双全纯于复欧氏空间，从而在所有复维数上正面解决Yau的单值化猜想。该结果若成立，将为正曲率Kähler几何提供基本分类结论。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"对象为完备连通非紧Kähler流形，全纯双截曲率严格正。",
"声称该流形双全纯于复欧氏空间。",
"作者称在所有复维数上正面解决Yau的单值化猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "几何与拓扑",
"interest": []
},
{
"id": "1595f391aa265ff7",
"section": "papers",
"category": "代数与表示论",
"title": "The Blockwise Alperin Weight Conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the numerical blockwise Alperin weight conjecture for every finite group and every prime p. For each p-block B, the number of irreducible Brauer characters in B equals the number of conjugacy classes of B-weights.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Blockwise Alperin Weight Conjecture",
"titleZh": "分块Alperin权重猜想",
"details": {
"overview": "稿件研究有限群表示论中的分块Alperin权重猜想。作者声称对每个有限群和每个素数p证明该猜想的数值形式：对每个p-块B，B中不可约Brauer特征标的个数等于B-权重的共轭类个数。该结果若成立，将统一处理该猜想的所有情形。该手稿为AI产生，尚未经独立审查或同行评议。",
"keyPoints": [
"声称对每个有限群和每个素数p证明分块Alperin权重猜想的数值形式。",
"结论为每个p-块B中不可约Brauer特征标数等于B-权重共轭类数。",
"稿件为AI产生，尚未经独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "群论与表示论",
"interest": []
},
{
"id": "146902b179cd3d7e",
"section": "papers",
"category": "代数与表示论",
"title": "Lech's multiplicity conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove Lech's multiplicity conjecture: Hilbert–Samuel multiplicity cannot decrease under a flat local homomorphism of nonzero Noetherian local rings. The result holds in arbitrary dimension, with no restrictions on the residue fields or characteristics.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Lech's multiplicity conjecture",
"titleZh": "Lech 重数猜想",
"details": {
"overview": "稿件提出证明 Lech 重数猜想：在非零 Noether 局部环的平坦局部同态下，Hilbert–Samuel 重数不会下降。摘要表示该结果在任意维数下成立，且对剩余域或特征没有限制。研究意义在于若成立，将为交换代数中重数沿平坦形变的单调性提供一般性结论。需注意该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者声称证明 Lech 重数猜想：平坦局部同态下 Hilbert–Samuel 重数不下降。",
"结果声称适用于任意维数，且不限制剩余域或特征。",
"手稿为 AI 产生，尚未完成独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "交换代数",
"interest": []
},
{
"id": "1441c130f4ad53f7",
"section": "papers",
"category": "组合数学与图论",
"title": "A counterexample to the Colin de Verdière chromatic conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove the Colin de Verdière chromatic conjecture by constructing graphs whose chromatic number exceeds their Colin de Verdière invariant by more than one. The examples have independence number at most two. In fact, their ordinary fractional chromatic number also exceeds their Colin de Verdière invariant by more than one.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A counterexample to the Colin de Verdière chromatic conjecture",
"titleZh": "Colin de Verdière 色数猜想的一个反例",
"details": {
"overview": "稿件提出构造反例否定 Colin de Verdière 色数猜想：所构造图的色数超过其 Colin de Verdière 不变量不止一。摘要还称这些例子的独立数至多为二，且普通分数色数也超过该不变量不止一。研究意义在于若成立，将推翻该猜想的一般形式，并涉及图不变量与色数之间的定量关系。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者构造图使色数超过 Colin de Verdière 不变量不止一，否定该猜想。",
"所构造例子的独立数至多为二。",
"其普通分数色数也超过该不变量不止一。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "13853a284de65cbc",
"section": "news",
"category": "行业新闻",
"title": "Introducing MentalHealthBench",
"summary": "该消息介绍 MentalHealthBench，一个由专家参与构建的基准，用于评估 AI 在贴近现实的心理健康对话中给出的回复是否有帮助且安全。",
"url": "https://openai.com/index/introducing-mentalhealthbench",
"date": "2026-09-23",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-23T10:00:00+00:00",
"titleEn": "Introducing MentalHealthBench",
"titleZh": "推出 MentalHealthBench",
"details": {
"overview": "该消息介绍 MentalHealthBench，一个由专家参与构建的基准，用于评估 AI 在贴近现实的心理健康对话中给出的回复是否有帮助且安全。当前收录材料仅给出这一概述，未说明基准的题目构成、评分方式或验证结果，相关细节需以原始发布为准。",
"keyPoints": [
"MentalHealthBench 是面向心理健康对话的评估基准",
"关注 AI 回复是否有帮助且安全",
"由专家参与构建，当前收录材料未提供具体评分方法"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "126b5500853cfa35",
"section": "papers",
"category": "代数与表示论",
"title": "A Counterexample to the Group-Ring Determinant Conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We disprove the unrestricted group-ring Determinant Conjecture. We construct a finitely generated group G and a square matrix over $`\\mathbb Z[G]`$ that is invertible over $`\\mathbb Q[G]`$ and has Fuglede–Kadison determinant strictly between zero and one. The logarithmic integral defining the determinant is finite.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A Counterexample to the Group-Ring Determinant Conjecture",
"titleZh": "群环行列式猜想的一个反例",
"details": {
"overview": "稿件提出否定无限制群环行列式猜想：构造一个有限生成群 G 以及 Z[G] 上的方阵，该矩阵在 Q[G] 上可逆，且其 Fuglede–Kadison 行列式严格介于零与一之间。摘要还称定义该行列式的对数积分有限。研究意义在于若成立，将表明该猜想在一般群环设定下不成立。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者构造有限生成群 G 与 Z[G] 上方阵，否定无限制群环行列式猜想。",
"该矩阵在 Q[G] 上可逆，Fuglede–Kadison 行列式严格在 0 与 1 之间。",
"摘要称定义行列式的对数积分有限。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数与群论",
"interest": []
},
{
"id": "116e372c81ab2f09",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Universal strong Kadison–Kastler stability",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that sufficiently close unital von Neumann algebras are conjugate by a unitary arbitrarily close to the identity. The tolerance depends only on the prescribed distance of that unitary from the identity, uniformly over all algebras, representations, and Hilbert spaces. This resolves the strong Kadison–Kastler conjecture.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Universal strong Kadison–Kastler stability",
"titleZh": "通用强 Kadison–Kastler 稳定性",
"details": {
"overview": "稿件提出证明强 Kadison–Kastler 猜想：充分接近的单位 von Neumann 代数可由任意接近恒等元的酉元共轭。摘要称容差只依赖于该酉元与恒等元的给定距离，并对所有代数、表示和 Hilbert 空间一致成立。研究意义在于若成立，将为算子代数扰动稳定性提供统一定量结论。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者声称证明强 Kadison–Kastler 猜想。",
"接近的单位 von Neumann 代数可由接近恒等元的酉元共轭。",
"容差仅依赖酉元与恒等元的距离，并对所有代数、表示和 Hilbert 空间一致。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "算子代数",
"interest": []
},
{
"id": "114083c6a0c6a415",
"section": "papers",
"category": "几何与拓扑",
"title": "Translative covering densities of order n log n",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Translative-covering-densities-of-order-n-log-n-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every sufficiently large dimension n, we construct a centrally symmetric convex body whose translative covering density exceeds $`c n\\log n`$, where c > 0 is absolute. This disproves the existence of a universal linear upper bound and matches the order of Rogers' upper bound.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Translative covering densities of order n log n",
"titleZh": "阶为 n log n 的平移覆盖密度",
"details": {
"overview": "稿件针对充分大的维数 n，构造中心对称凸体，使其平移覆盖密度超过 c n log n，其中 c 为绝对常数。摘要表示这否定了存在通用线性上界的可能性，并与 Rogers 上界的阶相匹配。研究意义在于若成立，将刻画高维平移覆盖密度可达到的阶。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"对充分大维数 n，构造中心对称凸体使平移覆盖密度超过 c n log n。",
"该结果否定通用线性上界的存在。",
"所构造密度的阶与 Rogers 上界相匹配。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "凸几何与离散几何",
"interest": []
},
{
"id": "0f952aab2292404e",
"section": "papers",
"category": "分析与偏微分方程",
"title": "Universal optimality of the triangular lattice",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove universal energy minimality for the triangular lattice in the plane. Among locally finite configurations of centered density one, it minimizes the lower limit of centered-ball energy averages for every nonnegative completely monotone function of squared distance, including when the energy is infinite. We also prove triangular minimality for planar logarithmic and Riesz renormalized energies, with $`0\\lt s\\lt 2`$ in the Riesz case, and the corresponding jellium minima. The proof uses sharp Gaussian Fourier bounds, positive mixtures, and heat-kernel comparison.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Universal optimality of the triangular lattice",
"titleZh": "三角格的通用最优性",
"details": {
"overview": "稿件提出证明平面三角格的通用能量极小性：在中心密度为一的局部有限构型中，对任意非负完全单调的平方距离函数，三角格最小化中心球能量平均的下极限，包括能量为无穷的情形。摘要还称证明了平面对数能量与 Riesz 重整化能量（Riesz 情形 00 仅依赖于 d。摘要表示这正面解决了高维 Erdős 不同距离猜想。研究意义在于若成立，将为高维点集的不同距离数量提供与维数相关的下界。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"对每个固定 d≥3，证明 ℝd 中 n 个不同点至少确定 c_d n^{2/d} 个不同距离。",
"常数 c_d 仅依赖于维数 d。",
"摘要称这正面解决高维 Erdős 不同距离猜想。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "097ce3bcc74417b0",
"section": "papers",
"category": "几何与拓扑",
"title": "A nine-dimensional counterexample to Borsuk's covering assertion",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-nine-dimensional-counterexample-to-Borsuks-covering-assertion-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "The compact set of rank-one orthogonal projectors on ℝ4, with the Frobenius metric, cannot be covered by ten sets of strictly smaller diameter. It therefore gives a counterexample to Borsuk's conjecture in dimension nine.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A nine-dimensional counterexample to Borsuk's covering assertion",
"titleZh": "Borsuk 覆盖断言的一个九维反例",
"details": {
"overview": "稿件考虑 ℝ4 上秩一正交投影算子按 Frobenius 度量构成的紧集，声称该集合不能被十个直径严格更小的集合覆盖，因此给出 Borsuk 猜想在九维的反例。研究意义在于若成立，将否定 Borsuk 猜想在九维的覆盖断言。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者使用 ℝ4 上秩一正交投影算子的紧集构造反例。",
"该集合不能被十个直径严格更小的集合覆盖。",
"摘要称这给出 Borsuk 猜想在九维的反例。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "凸几何与离散几何",
"interest": []
},
{
"id": "060c181b6e574554",
"section": "papers",
"category": "组合数学与图论",
"title": "A proof of Seymour’s second-neighborhood conjecture",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that every nonempty finite oriented graph has a vertex with at least as many vertices at directed distance two as at directed distance one. This resolves Seymour's second neighborhood conjecture positively.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "A proof of Seymour’s second-neighborhood conjecture",
"titleZh": "Seymour 第二邻域猜想的一个证明",
"details": {
"overview": "稿件提出证明每个非空有限有向图都存在一个顶点，其有向距离二的顶点数至少不少于有向距离一的顶点数。摘要表示这正面解决了 Seymour 第二邻域猜想。研究意义在于若成立，将为有向图中第二邻域与第一邻域的计数关系提供一般性结论。该手稿为 AI 产生，收录不表示已完成独立审查或同行评议。",
"keyPoints": [
"作者声称证明每个非空有限有向图存在顶点，其距离二顶点数不少于距离一顶点数。",
"摘要称这正面解决 Seymour 第二邻域猜想。",
"手稿为 AI 产生，尚未完成独立审查或同行评议。"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "组合数学与图论",
"interest": []
},
{
"id": "04090c43eedec02e",
"section": "papers",
"category": "理论计算机科学",
"title": "One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/One-Sample-Suffices-for-Matroid-Prophet-Inequalities-against-an-Almighty-Adversary-September-23-2026/final.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove that one independent sample per element suffices for a constant-competitive prophet inequality on every finite matroid. The guarantee holds even when the arrival-order adversary observes all samples, all online values, and the algorithm's entire random seed. The rule needs no description of the value distributions and achieves the absolute competitive ratio $`2^{-310}`$.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary",
"titleZh": "对抗全能对手的拟阵先知不等式：单样本即足够",
"details": {
"overview": "稿件研究拟阵上的先知不等式问题：每个元素只需一个独立样本，作者声称即可在任意有限拟阵上获得常数竞争比。摘要表示，即使到达顺序对手能看到全部样本、全部在线取值以及算法的整个随机种子，该保证仍成立；规则无需知道取值分布，绝对竞争比为2^{-310}。研究意义在于把样本需求降到每元素一个，并强化了对手能力假设。",
"keyPoints": [
"每个元素仅需一个独立样本即可构造规则",
"对手可观察样本、在线取值与算法随机种子",
"无需分布描述，声称绝对竞争比为2^{-310}"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "0272fb020bc2bedc",
"section": "papers",
"category": "几何与拓扑",
"title": "The metric Blaschke theorem",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-metric-Blaschke-theorem-September-23-2026/paper.pdf",
"date": "2026-09-23",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We prove the metric Blaschke conjecture: every connected closed smooth Riemannian manifold of positive dimension whose global injectivity radius equals its diameter is, up to scale, a standard compact rank-one symmetric space.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The metric Blaschke theorem",
"titleZh": "度量 Blaschke 定理",
"details": {
"overview": "稿件提出并证明度量 Blaschke 猜想：任何正维数的连通闭光滑黎曼流形，若其整体单射半径等于直径，则在不计尺度意义下是标准紧秩一对称空间。摘要只给出这一结论性陈述，未展开证明思路或技术细节。该结果把经典 Blaschke 型刻画推广到度量设定，作者声称完成了完整分类。",
"keyPoints": [
"研究对象为单射半径等于直径的闭黎曼流形",
"声称结论为不计尺度等于标准紧秩一对称空间",
"当前收录摘要未给出证明方法或技术细节"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "fd8a261787dd4a8b",
"section": "news",
"category": "模型动态",
"title": "Transformers now runs llama.cpp quants",
"summary": "该消息标题称 Transformers 现在可以运行 llama.cpp 的量化格式。",
"url": "https://huggingface.co/blog/transformers-llama-cpp-quants",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "Hugging Face 官方博客",
"publishedAt": "2026-09-22T00:00:00+00:00",
"titleEn": "Transformers now runs llama.cpp quants",
"titleZh": "Transformers 现已支持运行 llama.cpp 量化格式",
"details": {
"overview": "该消息标题称 Transformers 现在可以运行 llama.cpp 的量化格式。当前收录材料未提供正文内容，因此无法确认支持的具体量化类型、使用方式或限制条件，相关信息需以原始发布为准。",
"keyPoints": [
"标题称 Transformers 可运行 llama.cpp 量化格式",
"原文无正文，具体量化类型与用法不明",
"适用范围与限制需以原始发布为准"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "fc5adbe168263145",
"section": "news",
"category": "行业新闻",
"title": "Why Deploying Physical AI at Scale Demands Safety at Every Layer",
"summary": "文章讨论物理AI从研究走向大规模部署时面临的安全问题。",
"url": "https://blogs.nvidia.com/blog/physical-ai-halos-safety/",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "NVIDIA 官方博客",
"publishedAt": "2026-09-21T16:00:46+00:00",
"titleEn": "Why Deploying Physical AI at Scale Demands Safety at Every Layer",
"titleZh": "为何大规模部署物理AI需要每一层都具备安全性",
"details": {
"overview": "文章讨论物理AI从研究走向大规模部署时面临的安全问题。原文引用ABI Research预测2035年3至5级自动驾驶汽车保有量将达4900万辆，Omdia估计2026至2035年间约6000万台工业机器人将被部署。随着这些机器进入道路、工厂、仓库等与人共享的环境，作者提出安全需贯穿各层。摘要未展开具体安全框架与措施，细节不足。",
"keyPoints": [
"引用ABI Research预测2035年3至5级自动驾驶汽车保有量达4900万辆",
"引用Omdia估计2026至2035年约6000万台工业机器人将部署",
"指出机器进入与人共享环境，强调各层安全的重要性"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "fbe63401452add5a",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.7 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.7",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T07:00:44+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.7 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.7 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "ed2a480a4d32575c",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.2 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.2",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-21T23:02:34+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.2 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.2 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "eb2871a16fec6b8c",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.156.0-alpha.16 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.156.0-alpha.16",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-21T16:51:16+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.156.0-alpha.16 测试版发布",
"details": {
"overview": "Codex CLI 0.156.0-alpha.16 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "e8ff2dcaa8321b90",
"section": "news",
"category": "行业新闻",
"title": "NVIDIA Launches DSX Ready to Qualify Power and Cooling Products for AI Factories",
"summary": "文章介绍NVIDIA推出DSX Ready计划，用于认证适配AI工厂的供电与冷却产品。",
"url": "https://blogs.nvidia.com/blog/dsx-ready-ai-factories-power-cooling/",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "NVIDIA 官方博客",
"publishedAt": "2026-09-21T18:00:07+00:00",
"titleEn": "NVIDIA Launches DSX Ready to Qualify Power and Cooling Products for AI Factories",
"titleZh": "NVIDIA推出DSX Ready，为AI工厂的供电与冷却产品提供认证",
"details": {
"overview": "文章介绍NVIDIA推出DSX Ready计划，用于认证适配AI工厂的供电与冷却产品。原文指出每座AI工厂都需要与其计算架构匹配的供电和冷却，随着AI基础设施扩张，电力、冷却、水资源、场地和电网约束正影响建设者可部署的规模。选择符合整体工厂设计的产品有助于把算力转化为有用的AI产出。摘要未说明认证标准与覆盖范围。",
"keyPoints": [
"NVIDIA推出DSX Ready，面向AI工厂供电与冷却产品认证",
"原文称电力、冷却、水、场地与电网约束影响AI基础设施部署",
"目标是让产品匹配整体工厂设计，把算力转化为AI产出"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "e61ad5a380a226fe",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.3 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.3",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T01:38:20+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.3 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.3 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "df461b676e19e50c",
"section": "chatgpt",
"category": "功能更新",
"title": "Create flashcards in ChatGPT",
"summary": "OpenAI宣布ChatGPT新增创建互动抽认卡功能。",
"url": "https://help.openai.com/en/articles/6825453-chatgpt-release-notes#create-flashcards-in-chatgpt",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "ChatGPT 官方发布说明",
"titleEn": "Create flashcards in ChatGPT",
"titleZh": "在ChatGPT中创建抽认卡",
"details": {
"overview": "OpenAI宣布ChatGPT新增创建互动抽认卡功能。用户可请求就某学习主题生成抽认卡，或上传笔记让ChatGPT转换。点击卡片可翻转，选择✔️表示已掌握，选择❌则稍后再练；还可打乱顺序练习。抽认卡自动保存在资料库中，可再次打开或让ChatGPT调出复习。该功能在移动端和网页端向所有ChatGPT套餐开放。",
"keyPoints": [
"可请求生成主题抽认卡，或上传笔记转换为抽认卡",
"点击翻转卡片，用✔️或❌标记掌握情况并打乱顺序练习",
"抽认卡自动保存至资料库，移动端和网页端全套餐可用"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "d0163db52f5092a2",
"section": "papers",
"category": "几何与拓扑",
"title": "The Mahler Conjecture for General Convex Bodies",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026/paper.pdf",
"date": "2026-09-22",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the Mahler conjecture for general convex bodies positively. For every convex body $`K\\subset\\mathbb R^n`$, n ≥ 1, with Santaló point $`s(K)`$, $`|K|\\,|(K-s(K))^\\circ|\\ge (n+1)^{n+1}/(n!)^2`$, with equality exactly for simplices.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The Mahler Conjecture for General Convex Bodies",
"titleZh": "一般凸体的 Mahler 猜想",
"details": {
"overview": "稿件声称正面解决一般凸体的 Mahler 猜想：对任意 n≥1 的凸体 K⊂R^n，以 Santaló 点 s(K) 为基准，体积与其极体体积之积不小于 (n+1)^{n+1}/(n!)^2，且等号恰在单纯形时成立。摘要仅陈述结论与等号情形，未说明证明路线。该问题属凸几何中的经典体积积不等式，作者声称给出完整解答。",
"keyPoints": [
"声称对任意维数的一般凸体证明体积积下界",
"下界为 (n+1)^{n+1}/(n!)^2",
"等号情形恰为单纯形"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "cf795aead209d64d",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.8 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.8",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T12:34:27+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.8 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.8 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "baea377a3e2d78e8",
"section": "news",
"category": "行业新闻",
"title": "Jun Kim, oMLX creator and maintainer, joins Hugging Face to support the MLX community",
"summary": "该消息称oMLX的创建者兼维护者Jun Kim加入Hugging Face，以支持MLX社区。",
"url": "https://huggingface.co/blog/omlx",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "Hugging Face 官方博客",
"publishedAt": "2026-09-22T00:00:00+00:00",
"titleEn": "Jun Kim, oMLX creator and maintainer, joins Hugging Face to support the MLX community",
"titleZh": "oMLX创建者兼维护者Jun Kim加入Hugging Face，支持MLX社区",
"details": {
"overview": "该消息称oMLX的创建者兼维护者Jun Kim加入Hugging Face，以支持MLX社区。原文仅有标题，未提供其具体职责、加入时间、oMLX项目后续安排或Hugging Face相关计划等信息，因此无法进一步说明这一人事变动对MLX生态的实际影响，需以官方后续发布为准。",
"keyPoints": [
"oMLX创建者兼维护者Jun Kim加入Hugging Face",
"官方表述其目的是支持MLX社区",
"当前收录材料未提供具体职责与项目安排"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "b5b9e2f370441823",
"section": "news",
"category": "行业新闻",
"title": "How UK AISI and EvalEval Are Making Benchmark Results Reproducible",
"summary": "该条目介绍英国AI安全研究所（UK AISI）与EvalEval在使基准测试结果可复现方面的工作。",
"url": "https://huggingface.co/blog/evaleval-aisi",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "Hugging Face 官方博客",
"publishedAt": "2026-09-22T00:00:00+00:00",
"titleEn": "How UK AISI and EvalEval Are Making Benchmark Results Reproducible",
"titleZh": "英国AISI与EvalEval如何让基准测试结果可复现",
"details": {
"overview": "该条目介绍英国AI安全研究所（UK AISI）与EvalEval在使基准测试结果可复现方面的工作。原文仅有标题，未说明双方合作的具体方法、涉及的基准测试、复现流程或已发布成果，因此无法展开技术细节。相关结论与工具需以官方原始发布内容为准。",
"keyPoints": [
"主题为英国AISI与EvalEval提升基准结果可复现性",
"当前收录材料未提供具体方法、基准或成果",
"细节需以官方原始发布为准"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "ab380cad68b95473",
"section": "news",
"category": "行业新闻",
"title": "Priorities and principles for effective third party assessments",
"summary": "OpenAI发文阐述其对前沿模型与防护措施开展严格、安全且独立的第三方AI安全评估的优先事项与原则。",
"url": "https://openai.com/index/priorities-principles-third-party-assessments",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "OpenAI 官方新闻",
"publishedAt": "2026-09-22T00:00:00+00:00",
"titleEn": "Priorities and principles for effective third party assessments",
"titleZh": "有效第三方评估的优先事项与原则",
"details": {
"overview": "OpenAI发文阐述其对前沿模型与防护措施开展严格、安全且独立的第三方AI安全评估的优先事项与原则。原文摘要仅说明这一总体立场，未列出具体原则条目、评估范围、实施时间或与外部机构的安排，因此无法进一步说明各项原则的内容与落地方式。",
"keyPoints": [
"OpenAI提出第三方AI安全评估的优先事项与原则",
"强调评估应严格、安全且独立，对象为前沿模型与防护措施",
"原文未列出具体原则条目与实施安排"
],
"editorialNote": "根据官方 RSS 所附摘要或正文节选整理，中文为辅助阅读；材料未列出的细节请打开原始文章核实，不能据此断言原文没有说明。"
},
"sourceMaterial": "官方 RSS 所附摘要或正文节选",
"interest": []
},
{
"id": "a35ed3911159ed48",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.4 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.4",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T03:01:53+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.4 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.4 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "7f57e08c39facb04",
"section": "codex",
"category": "功能更新",
"title": "Codex app 26.917",
"summary": "Codex应用26.917版本更新日志列出新功能与修复。",
"url": "https://learn.chatgpt.com/docs/changelog",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "ChatGPT 与 Codex 官方变更日志",
"titleEn": "Codex app 26.917",
"titleZh": "Codex应用26.917版本",
"details": {
"overview": "Codex应用26.917版本更新日志列出新功能与修复。新增任务完成、权限请求和提问的通知声音设置，可选Default、Classic或None；macOS上还可选择系统声音或导入音频文件。修复方面，新增针对阻止应用启动的会话错误的登录恢复对话框，并在工作树设置完成后保留重命名对话框中的聊天标题。",
"keyPoints": [
"新增任务完成、权限请求与提问的通知声音设置",
"macOS支持选择系统声音或导入音频文件",
"新增登录恢复对话框，并修复重命名对话框聊天标题丢失"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "79456c8b13bbc6c9",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.6 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.6",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-22T05:50:02+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.6 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.6 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "73d0ddf74e89c5e4",
"section": "codex",
"category": "功能更新",
"title": "GPT-6 Sol and Luna in Codex and ChatGPT Work",
"summary": "OpenAI称GPT-6 Sol与GPT-6 Luna正逐步上线Codex和ChatGPT Work，token价格低于前代GPT-5.6。",
"url": "https://learn.chatgpt.com/docs/changelog",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "ChatGPT 与 Codex 官方变更日志",
"titleEn": "GPT-6 Sol and Luna in Codex and ChatGPT Work",
"titleZh": "Codex与ChatGPT Work中的GPT-6 Sol和Luna",
"details": {
"overview": "OpenAI称GPT-6 Sol与GPT-6 Luna正逐步上线Codex和ChatGPT Work，token价格低于前代GPT-5.6。Sol面向复杂编码与智能体工作流，Luna面向聚焦的高吞吐任务。两款模型向Plus、Pro、Business、Enterprise和Edu用户推出，Free和Go用户可在桌面应用使用Luna。可用性取决于推送与工作区设置，Enterprise管理员需启用；ChatGPT中仅在Work和Codex可用，不在Chat。",
"keyPoints": [
"GPT-6 Sol与Luna上线Codex和ChatGPT Work，token价格低于GPT-5.6",
"Sol用于复杂编码与智能体工作流，Luna用于高吞吐聚焦任务",
"Free和Go用户可在桌面应用使用Luna，Enterprise需管理员启用"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "6be9cf119678dca4",
"section": "papers",
"category": "几何与拓扑",
"title": "The symmetric Mahler conjecture and its equality cases",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf",
"date": "2026-09-22",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "We resolve the symmetric Mahler conjecture positively, including its equality classification. Every origin-symmetric convex body in ℝn has volume product at least $`4^n/n!`$, with equality exactly for invertible linear images of Hanner polytopes.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "The symmetric Mahler conjecture and its equality cases",
"titleZh": "对称 Mahler 猜想及其等号情形",
"details": {
"overview": "稿件声称正面解决对称 Mahler 猜想并完成等号分类：任意原点对称凸体在 R^n 中的体积积至少为 4^n/n!，等号恰在 Hanner 多面体的可逆线性像处取得。摘要只给出结论与等号刻画，未展开证明。该结果针对凸几何中对称体积积的经典猜想，作者声称同时给出下界与等号情形。",
"keyPoints": [
"声称原点对称凸体体积积下界为 4^n/n!",
"等号恰为 Hanner 多面体的可逆线性像",
"摘要未提供证明细节"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"subjectDetail": "数学论文",
"interest": []
},
{
"id": "6440c7934432d093",
"section": "codex",
"category": "功能更新",
"title": "GPT-6 Sol and Luna in Work and Codex",
"summary": "官方发布信息显示，GPT-6 Sol 和 GPT-6 Luna 被引入 ChatGPT Work 与 Codex，这两款模型与 Chat 中可用的模型相互独立。",
"url": "https://help.openai.com/en/articles/6825453-chatgpt-release-notes#gpt-6-sol-and-luna-in-work-and-codex",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "ChatGPT 官方发布说明",
"titleEn": "GPT-6 Sol and Luna in Work and Codex",
"titleZh": "GPT-6 Sol 与 Luna 登陆 ChatGPT Work 和 Codex",
"details": {
"overview": "官方发布信息显示，GPT-6 Sol 和 GPT-6 Luna 被引入 ChatGPT Work 与 Codex，这两款模型与 Chat 中可用的模型相互独立。Codex 桌面端会保留用户手动选择的模型，可用模型及推理强度选项取决于套餐与工作区设置。当前收录材料未提供模型能力、参数或评测细节，推出范围与限制需以原始发布为准。",
"keyPoints": [
"GPT-6 Sol 与 Luna 面向 ChatGPT Work 和 Codex，与 Chat 模型分开",
"Codex 桌面端保留用户手动选择的模型",
"可用模型与推理强度取决于套餐和工作区设置"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "3f18ee480c460bc9",
"section": "news",
"category": "行业新闻",
"title": "NVIDIA Isaac ROS 5.0 Advances Agentic, Open Source Robotics Development",
"summary": "原文指出，构建能在动态环境中感知、推理和行动的机器人应用，需要新的物理 AI 模型与工具。",
"url": "https://blogs.nvidia.com/blog/isaac-ros-5-0-agentic-open-source-robotics/",
"date": "2026-09-22",
"status": "依据官方原始发布记录整理；当时的推出范围和限制请以原文为准。",
"source": "NVIDIA 官方博客",
"publishedAt": "2026-09-22T12:00:41+00:00",
"titleEn": "NVIDIA Isaac ROS 5.0 Advances Agentic, Open Source Robotics Development",
"titleZh": "NVIDIA Isaac ROS 5.0 推进智能体化开源机器人开发",
"details": {
"overview": "原文指出，构建能在动态环境中感知、推理和行动的机器人应用，需要新的物理 AI 模型与工具。ROS 是 Open Robotics 的开源框架，用于帮助人们构建机器人。NVIDIA Isaac ROS 5.0 是基于 ROS 的 GPU 加速软件包集合，官方称其在相关活动上发布。原文摘要在此处截断，未给出具体功能、性能数据或适用范围，需以完整发布内容为准。",
"keyPoints": [
"Isaac ROS 5.0 是基于 ROS 的 GPU 加速软件包集合",
"面向在动态环境中感知、推理与行动的机器人应用",
"ROS 为 Open Robotics 的开源机器人框架"
],
"editorialNote": "根据所链接原始材料整理，中文为辅助阅读，请以原文为准。"
},
"interest": []
},
{
"id": "3aca485c78745c6d",
"section": "codex",
"category": "功能更新",
"title": "Codex CLI 0.157.0-alpha.1 测试版发布",
"summary": "Codex CLI 测试版版本发布；官方记录未列出详细的功能变更。",
"url": "https://github.com/openai/codex/releases/tag/rust-v0.157.0-alpha.1",
"date": "2026-09-22",
"status": "已发布的测试版本，不代表稳定版已开放。",
"source": "Codex GitHub Releases",
"publishedAt": "2026-09-21T18:08:16+00:00",
"releaseChannel": "prerelease",
"titleZh": "Codex CLI 0.157.0-alpha.1 测试版发布",
"details": {
"overview": "Codex CLI 0.157.0-alpha.1 测试版发布。该条官方 GitHub 发布记录只给出版本标识，没有列出可供核实的具体新增功能或修复。这里保留其发布时间和原始发布链接，方便追溯版本历史；不能据此推断桌面端已经具备某项能力。",
"keyPoints": [
"发布渠道：测试版",
"该条发布记录未提供详细变更清单"
],
"editorialNote": "仅整理该版本实际发布记录，不根据版本号推测功能。"
},
"interest": []
},
{
"id": "39bbcf904bce37b9",
"section": "papers",
"category": "几何与拓扑",
"title": "Symplectic Balls in Symmetric Polar Products",
"summary": "OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。",
"url": "https://github.com/openai/math/blob/main/preprints/Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026/paper.pdf",
"date": "2026-09-22",
"status": "AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。",
"abstractEnglish": "For every integer n ≥ 2 and every origin-symmetric convex body $`K\\subset\\mathbb R^n`$, we prove that the Gromov width of $`\\mathop{\\mathrm{int}}\\nolimits K\\times\\mathop{\\mathrm{int}}\\nolimits K^\\circ`$ is 4. We construct smooth symplectic embeddings of standard balls of every capacity $`0\\lt c\\lt 4`$ into this polar product. Volume preservation then resolves the symmetric Mahler conjecture positively in every dimension.",
"sourceRepository": "https://github.com/openai/math",
"license": "Apache-2.0",
"titleEn": "Symplectic Balls in Symmetric Polar Products",
"titleZh": "对称极积中的辛球",
"details": {
"overview": "稿件研究原点对称凸体 K 与其极体 K^∘ 的极积 int K × int K^∘ 的辛容量。作者声称对任意 n≥2 证明其 Gromov 宽度为 4，并构造容量在 0 到 4 之间每个标准球的平滑辛嵌入。摘要表示，借助体积保持可正面解决各维数的对称 Mahler 猜想。研究把辛嵌入与凸几何体积积不等式联系起来。",
"keyPoints": [
"声称极积 int K×int K^∘ 的 Gromov 宽度为 4",
"构造容量 0 |