{ "archive": { "archive": "math_research_01_of_08.zip", "sha256": "5c735b4c234043dbff9be6dc7ea1d96dab0535f80607fd87d1dcb23073bbcd54", "bytes": 69857537, "crc_ok": true, "files": 1697, "physical_work_folders": 113, "preprint_pdfs": 113, "groups": [ "032", "033", "034", "035", "036", "037", "038", "039", "040", "041", "042", "043", "044", "046", "047", "048", "049", "050", "051", "052", "053", "054", "055", "056", "057", "058", "059", "060", "062", "063", "064", "065", "066", "067", "068", "193", "194", "195", "196", "197", "198", "199", "200", "201", "202", "203", "204", "205", "206", "207", "208", "209", "210" ], "current_manuscripts": 113 }, "reading_policy": "Archive catalog parsed; PDFs opened structurally; only explicit read_detail entries represent actual reading.", "works": [ { "id": "032-01", "group": "032", "title": "The rational Hodge conjecture for CM abelian varieties", "pdf": "preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf", "folder": "preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026", "abstract_original": "We prove the rational Hodge conjecture for complex abelian varieties with complex multiplication: every rational Hodge class on such a variety is a rational linear combination of algebraic cycle classes. As consequences, we obtain the generalized Hodge conjecture for CM abelian varieties, the Tate conjecture for abelian varieties over finite fields, and the Hodge standard conjecture for abelian varieties in arbitrary characteristic.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 762, "coverage": "intro_theorems", "read_detail": { "work": "032-01", "pages": "1–4", "scope": "Главная теорема и геометрическая архитектура введения" }, "pages": 53, "sha256": "6e3e66a407773ad5091d4cb48d9b4dc55a69c58fb0948a88daf19f3bb21bf27b", "bundled_pdf": "sources/papers/032-01/paper.pdf", "local_href": "../math_sources/math_research_01_of_08/preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "032-02", "group": "032", "title": "Algebraic Kuga–Satake correspondences and Hodge conjectures on a K3 quadratic locus", "pdf": "preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026/paper.pdf", "folder": "preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026", "abstract_original": "We prove the rational Hodge and generalized Hodge conjectures in every cohomological degree of every self-power of a projective complex K3 surface whose transcendental quadratic space, with its cup-product form, admits a rational isometric embedding in $`\\mathbb U_{\\mathbb Q}^{\\oplus2}\\perp\\langle-1\\rangle^4`$. This includes every ample P -polarized K3 surface, including all Picard jumps, for $`P=\\mathbb U\\oplus D_8(-1)\\oplus D_4(-1)`$. On this locus we construct algebraic correspondences inducing every prescribed standard even-Clifford Kuga–Satake tensor. More generally, for any projective complex K3 surface, algebraicity of one exact standard even-Clifford Kuga–Satake tensor implies both conjectures for every self-power.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 771, "coverage": "catalog_only", "read_detail": null, "pages": 63, "sha256": "c9fde2b758f255059c3aa153c73971330b18ed67ddd24d3272a1c793cc16dffd", "bundled_pdf": "sources/papers/032-02/paper.pdf", "local_href": "../math_sources/math_research_01_of_08/preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Algebraic-Kuga-Satake-correspondences-and-Hodge-conjectures-on-a-K3-quadratic-locus-September-30-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "032-03", "group": "032", "title": "Weil classes and Hodge classes on abelian powers", "pdf": "preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf", "folder": "preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026", "abstract_original": "We prove the rational Hodge conjecture in every codimension on every self-power of a complex abelian sixfold with an imaginary-quadratic action and a compatible polarization whose rational homological Hermitian form is hyperbolic of signature $`(3,3)`$. We also prove it in every codimension on every self-power of a complex abelian variety of dimension at most five admitting an imaginary-quadratic action. Both results include nonsimple varieties and special periods with additional endomorphisms. The proof uses the companion theorem on the rational Hodge conjecture for CM abelian varieties.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 780, "coverage": "catalog_only", "read_detail": null, "pages": 94, "sha256": "c035db86eb70657344f5b43f1a1b9a39952b946a9dca4cde21cf047300dfdbde", "bundled_pdf": "sources/papers/032-03/paper.pdf", "local_href": "../math_sources/math_research_01_of_08/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-October-6-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "032-04", "group": "032", "title": "Abelian covers, Gale correspondences, and the Hodge conjecture for powers", "pdf": "preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026/paper.pdf", "folder": "preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026", "abstract_original": "We prove the rational Hodge conjecture on every self-power of the Jacobian at each tensor Hodge-generic point of the full marked variation of a connected abelian cover of curves. This holds in every base genus and for every compatible branching pattern. For any CM abelian variety, the conclusion also holds for every self-power of its product with the Jacobian, on the same Hodge-generic locus. We also prove the conjecture on every self-power of a very general member of the full smooth labelled family of diagonal complete intersections cut out by at most two equations of a common degree, in every dimension and every degree at least two.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 789, "coverage": "catalog_only", "read_detail": null, "pages": 47, "sha256": "3467c8077855a568ec75b4f4c025fa50024cc9944df46346c57fe499fae6c8e8", "bundled_pdf": "sources/papers/032-04/paper.pdf", "local_href": "../math_sources/math_research_01_of_08/preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Abelian-covers-Gale-correspondences-and-the-Hodge-conjecture-for-powers-October-6-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "032-05", "group": "032", "title": "A Conditional Reduction for Algebraic Kuga–Satake Correspondences", "pdf": "preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf", "folder": "preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026", "abstract_original": "For a polarized K3 surface whose primitive cohomology has full orthogonal Hodge group, one algebraic correspondence inducing a nonzero map from that cohomology to the second cohomology of an abelian variety suffices to recover the prescribed full Kuga–Satake correspondence. We give an equivalent condition using holomorphic one-forms on a generically finite surface cover. If this input holds very generally in a polarized component, the prescribed correspondence is algebraic throughout that component, for every choice of standard data on the transcendental part. The existence of the initial correspondence remains a hypothesis.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 798, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "e59953bdc640de5f69ef85650dfe1118ec8a68848867497d332e94ba385024d8", "bundled_pdf": "sources/papers/032-05/paper.pdf", "local_href": "../math_sources/math_research_01_of_08/preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "033-01", "group": "033", "title": "Orbifold and logarithmic Iitaka subadditivity", "pdf": "preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026/paper.pdf", "folder": "preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026", "abstract_original": "We prove Campana's orbifold Iitaka subadditivity conjecture for rational simple normal crossing boundaries on compact manifolds in Fujiki class $`\\mathcal C`$, including coefficient one. Ordinary and logarithmic subadditivity follow.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 814, "coverage": "catalog_only", "read_detail": null, "pages": 55, "sha256": "b143366cc99615e19783fa075caafd8c9565e7bf5a554a612e086657c2aeeb79", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Orbifold-and-logarithmic-Iitaka-subadditivity-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "033-02", "group": "033", "title": "Logarithmic Kodaira dimension and whole-fiber variation", "pdf": "preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf", "folder": "preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026", "abstract_original": "We prove the logarithmic Iitaka–Viehweg inequality for projective surjective morphisms with connected fibers between smooth complex quasi-projective varieties whose base has nonnegative logarithmic Kodaira dimension. The variation measures the birational field of definition of the whole geometric generic fiber. This resolves Popa's logarithmic variation conjecture positively.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 823, "coverage": "catalog_only", "read_detail": null, "pages": 75, "sha256": "9b1b750b309e5c5a37fa1b472836f98c8eeffe69e4e7604452de18128a479e4a", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "033-03", "group": "033", "title": "The reverse logarithmic Kodaira inequality and additivity", "pdf": "preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf", "folder": "preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026", "abstract_original": "We prove the reverse logarithmic Kodaira inequality for a surjective connected-fiber morphism $`f:(X,E)\\to(Y,D)`$ of smooth projective reduced simple-normal-crossing pairs, with $`\\mathop{\\mathrm{Supp}}\\nolimits (f^*D)\\subseteq\\mathop{\\mathrm{Supp}}\\nolimits E`$, such that X and every boundary stratum are smooth over $`Y\\setminus\\mathop{\\mathrm{Supp}}\\nolimits D`$. Together with logarithmic subadditivity, the inequality gives additivity, including both negative-infinity cases. This resolves Popa's logarithmic additivity conjecture positively in the projective reduced-SNC, stratum-smooth setting.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 832, "coverage": "catalog_only", "read_detail": null, "pages": 51, "sha256": "499df173e9f8ba2d88b644514c4ea3a797d5c00de4148bac246f7a4c857094f9", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "033-04", "group": "033", "title": "Projective Hodge lines and ordinary Iitaka subadditivity", "pdf": "preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026/paper.pdf", "folder": "preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026", "abstract_original": "We prove the ordinary Iitaka subadditivity conjecture for surjective projective morphisms with connected fibers between smooth connected projective varieties over algebraically closed fields of characteristic zero. If F is the geometric generic fiber of $`f:X\\to Z`$, then $`\\kappa(X)\\geq\\kappa(F)+\\kappa(Z)`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 841, "coverage": "catalog_only", "read_detail": null, "pages": 40, "sha256": "564a98c625b94ef479a6690bed65451fee18c47c69c23e5d9e1f4fd181deca9a", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Projective-Hodge-lines-and-ordinary-Iitaka-subadditivity-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "033-05", "group": "033", "title": "B-semiampleness for compact log-smooth Kähler fibrations", "pdf": "preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf", "folder": "preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026", "abstract_original": "We prove the compact log-smooth Kähler case of b-semiampleness. Let $`f:Y\\to X`$ be a surjective holomorphic map with connected fibers between smooth compact connected Kähler manifolds, and let Δ be an effective rational divisor with simple normal crossing support and coefficients in $`[0,1]`$, with $`K_Y+\\Delta\\sim_{\\mathbb Q}f^*L`$ for $`L\\in\\mathop{\\mathrm{Pic}}\\nolimits (X)_{\\mathbb Q}`$. There is a smooth compact Kähler modification $`S\\to X`$ for which the threshold-moduli line satisfies $`M_{S_1}=\\nu^*M_S`$ in $`\\mathop{\\mathrm{Pic}}\\nolimits (S_1)_{\\mathbb Q}`$ for every smooth compact Kähler modification $`\\nu:S_1\\to S`$, and some positive multiple of M S is represented by a holomorphic line bundle generated by global sections. Horizontal components of coefficient one are allowed; neither projectivity nor a Campana orbifold Iitaka hypothesis is assumed.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 850, "coverage": "catalog_only", "read_detail": null, "pages": 38, "sha256": "afad4b593eede2ddf61795187a33ccddbf38dd470c67580982682623ae351d19", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-01", "group": "034", "title": "Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity", "pdf": "preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf", "folder": "preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026", "abstract_original": "Assume logarithmic Iitaka subadditivity for surjective morphisms with connected fibers between smooth projective complex varieties with compatible reduced simple normal crossing boundaries. We prove log abundance for normal irreducible compact Kähler spaces in every dimension: for a log canonical pair $`(X,\\Delta)`$ with effective rational boundary and $`K_X+\\Delta`$ ℚ-Cartier, analytic nefness of $`K_X+\\Delta`$ implies semiampleness.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 866, "coverage": "catalog_only", "read_detail": null, "pages": 157, "sha256": "46adc5be1070213b3a553dbd691b61daffcb734e5616b627e26a573a39e44dd8", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-02", "group": "034", "title": "Uniform indices for semi-log-canonical log Calabi–Yau pairs", "pdf": "preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026/uniform-slc-index.pdf", "folder": "preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026", "abstract_original": "We prove a uniform index theorem for connected projective semi-log-canonical log Calabi–Yau pairs in every fixed dimension at least four over an algebraically closed field of characteristic zero. For boundary coefficients in a fixed finite rational set, a single multiple of the log canonical divisor is Cartier and linearly trivial. The multiple depends only on the dimension and coefficient set, not on the number of irreducible components. Together with the established theorem in dimensions at most three, this resolves the finite-rational-coefficient semi-log-canonical index conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 875, "coverage": "catalog_only", "read_detail": null, "pages": 42, "sha256": "588f61707a03040f0265823b76aa32e17f238bfed772f79bdcd8f9867746a126", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026/uniform-slc-index.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-indices-for-semi-log-canonical-log-Calabi-Yau-pairs-October-5-2026/uniform-slc-index.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-03", "group": "034", "title": "Conditional good minimal models for compact Kähler fourfolds", "pdf": "preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "folder": "preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026", "abstract_original": "Assuming orbifold Iitaka subadditivity and abundance for nef fourfold adjoints of nonnegative Kodaira dimension, we prove the existence of good minimal models for globally strongly ℚ-factorial compact Kähler klt fourfold pairs with effective rational boundary and analytically pseudo-effective actual ℚ-Cartier adjoint. The ordinary fourfold minimal model program supplies the nef endpoint. We prove nonvanishing by fibration arguments and, in algebraic dimension zero, by singular metrics, holomorphic foliations, and extension from a reduced boundary. The projective abundance argument used in the proof is included in full.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 884, "coverage": "catalog_only", "read_detail": null, "pages": 139, "sha256": "eebddaadef6935c3072a8c1eb556a002bbab27788c337bbba2f9e579bc81b6d3", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-04", "group": "034", "title": "Log abundance in characteristic zero", "pdf": "preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf", "folder": "preprints/Log-abundance-in-characteristic-zero-September-24-2026", "abstract_original": "We prove the rational-boundary log abundance conjecture in every dimension over algebraically closed fields of characteristic zero: every nef ℚ-Cartier log canonical divisor on a projective log canonical pair with effective rational boundary is semiample. Over ℂ, the proof also establishes canonical nonvanishing for smooth projective varieties in every dimension.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 893, "coverage": "catalog_only", "read_detail": null, "pages": 85, "sha256": "87b191f75e8c852683847be18fb99e2a226e11e55967624c8d2bbba41c509be0", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-05", "group": "034", "title": "Minimal metrics and interior injectivity for nef adjoints", "pdf": "preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf", "folder": "preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026", "abstract_original": "Let $`(H,\\Theta)`$ be a projective complex klt pair with effective rational boundary and nef ℚ-Cartier adjoint. On any projective log resolution, minimal semipositive metrics on the pulled-back adjoint exist and have zero Lelong numbers everywhere. On smooth projective complex varieties, we also prove an H 1 -injectivity theorem for rational interior boundaries with simple-normal-crossing support when both endpoint bundles carry zero-Lelong semipositive metrics.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 902, "coverage": "catalog_only", "read_detail": null, "pages": 21, "sha256": "b2a7d738f44a3d34e5d22e0a7fb8a8d38e97b6e2858f6c77d70cb9b03193fbd6", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-06", "group": "034", "title": "Fourfold nonvanishing by minimal metrics and moving jets", "pdf": "preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf", "folder": "preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026", "abstract_original": "We prove canonical nonvanishing for smooth connected projective complex fourfolds: if K X is pseudo-effective, then $`H^0(X,mK_X)\\ne0`$ for some positive integer m .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 911, "coverage": "catalog_only", "read_detail": null, "pages": 38, "sha256": "1946d50201ab1ae0c02a6ba95143b55528b2525d45673a2985404aee4d8f2cb4", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-07", "group": "034", "title": "Lifting sections from the reduced support of an adjoint", "pdf": "preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf", "folder": "preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026", "abstract_original": "For a projective ℚ-factorial dlt pair with effective rational boundary over an algebraically closed field of characteristic zero, we prove that the adjoint has positive Iitaka dimension whenever a nonzero effective Cartier multiple is supported on the coefficient-one boundary and restricts to a semiample line bundle on its whole reduced support. This gives log abundance after nonvanishing in dimension at most four over ℂ.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 920, "coverage": "catalog_only", "read_detail": null, "pages": 40, "sha256": "ecbc1b8c73fefb32ddbd51ef6fcc0cb2a91e935bea46075c557f07bcc86fb9ed", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-08", "group": "034", "title": "Schnell fiber spaces and good canonical models", "pdf": "preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf", "folder": "preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026", "abstract_original": "We prove the Campana–Peternell inequality $`\\kappa(X)\\geq\\kappa(D)`$ for a smooth connected projective complex variety X and an effective Cartier divisor D whenever $`m_0K_X-D`$ is pseudo-effective for some positive integer m 0 . For an algebraic fiber space $`f\\colon X\\to Y`$ between smooth connected projective complex varieties, the hypothesis that $`m_0K_X-f^*H`$ is pseudo-effective with H ample Cartier gives $`\\kappa(X)=\\kappa(F)+\\dim Y`$ for a very general smooth fiber F , as well as nonzero sections of $`mK_X-f^*H`$ for all sufficiently large divisible m .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 929, "coverage": "catalog_only", "read_detail": null, "pages": 11, "sha256": "7abe2cb2832b55efb9d29c43441cc662848090c26a19c909e7fbef6e3ee1ce2a", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-09", "group": "034", "title": "Uniform log Iitaka fibrations and bounded moduli denominators", "pdf": "preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf", "folder": "preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026", "abstract_original": "For normal projective log canonical pairs over algebraically closed fields of characteristic zero, of fixed dimension d ≥ 5 and with effective boundary coefficients in a fixed finite rational set, we prove that one complete rounded pluricanonical system generates the full Iitaka field whenever the ℚ-Cartier log canonical divisor has nonnegative Kodaira dimension. Its degree depends only on the dimension and coefficient set. For the paper's normalized canonical bundle formulae over ℂ, we also bound the Cartier denominators of the moduli divisors on smooth projective determining models in terms of the dimension and coefficient set.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 938, "coverage": "catalog_only", "read_detail": null, "pages": 32, "sha256": "0fee79cbeaa3ae4f119c3ca2fc961e0b7c8af1b6853af22bb3cdcacf1b55a9d5", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-10", "group": "034", "title": "Uniform Pluricanonical Iitaka Fibrations", "pdf": "preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf", "folder": "preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026", "abstract_original": "We prove the effective Iitaka fibration conjecture in characteristic zero. For each dimension, one pluricanonical degree defines the Iitaka fibration of every smooth integral projective variety of that dimension and nonnegative Kodaira dimension over an algebraically closed field. The associated sections generate the full Iitaka function field.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 947, "coverage": "catalog_only", "read_detail": null, "pages": 44, "sha256": "88c226e29ee72119478882f48b674d5bd0d4813a331dfa35067fef758e0e4df8", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-11", "group": "034", "title": "Relative denominators and effective systems for log Calabi-Yau fibrations", "pdf": "preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf", "folder": "preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026", "abstract_original": "We prove uniform denominator and effective-system bounds for log Calabi-Yau fibrations from projective log canonical complex pairs of dimension at most four onto positive-dimensional bases, with boundary coefficients in a fixed finite rational set. The bounds give a uniform trivializing degree and a uniform b-Cartier multiple of the moduli b-divisor. When the base divisor is big, a uniform complete rounded adjoint system has section ratios generating the full base function field.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 956, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "a539053eb28e6c4d8aa1724d461504b215ec29a55ca57dd45f24a4b998dce623", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-12", "group": "034", "title": "Arithmetic Stein-degree bounds for log Calabi–Yau pairs", "pdf": "preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf", "folder": "preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026", "abstract_original": "Fix d ≥ 1 and t > 0. Let $`(X,B)`$ be an ordinary projective log canonical ℚ-pair of dimension d over a characteristic-zero field k , with X normal and integral, $`H^0(X,\\mathcal O_X)=k`$, B effective, and $`K_X+B\\sim_{\\mathbb Q}0`$. We prove that every prime component S of B with coefficient at least t satisfies $`[k_S:k]\\leq N(d,t)`$, where k S is the relative algebraic closure of k in $`k(S)`$. This also bounds the Stein degree of S over k , proving the contraction-to-a-point formulation of Birkar's Stein-degree conjecture for ordinary ℚ-pairs.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 965, "coverage": "catalog_only", "read_detail": null, "pages": 15, "sha256": "41101b5f371f3fde9ff08c3bcec93af68dc06ecb2fb74bf01a58b50f28a024e2", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-13", "group": "034", "title": "Uniform effective log Iitaka fibrations for fourfolds", "pdf": "preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf", "folder": "preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026", "abstract_original": "We prove the finite-rational-coefficient case of the effective log Iitaka conjecture in dimension four. For normal projective log canonical complex fourfolds with boundary coefficients in a fixed finite rational set and pseudo-effective rational Cartier adjoint, one uniform degree makes the complete rounded reflexive system nonempty and its section ratios generate the full Iitaka field. We also prove a uniform canonical index bound for projective klt complex fourfolds with rationally trivial canonical divisor.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 974, "coverage": "catalog_only", "read_detail": null, "pages": 52, "sha256": "8036215575dbf6199927ae50571f50d8e89928b091dc07fa723fec2cbfe5a41e", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "034-14", "group": "034", "title": "Abundance after nonvanishing for compact Kähler fourfolds", "pdf": "preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf", "folder": "preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026", "abstract_original": "We prove semiampleness of the actual ℚ-Cartier adjoint $`K_X+\\Delta`$ of a normal connected compact Kähler klt fourfold whenever it is analytically nef and some positive Cartier multiple has a nonzero section. The boundary is effective and rational; the fourfold need not be projective or ℚ-factorial. In Iitaka dimension zero, a positive Cartier multiple is the trivial holomorphic line bundle.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 983, "coverage": "catalog_only", "read_detail": null, "pages": 92, "sha256": "89b5dd1a939cd7a67bbc90c83fe34ac5398d08f9103aa1cf8351bb3825e09273", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "035-01", "group": "035", "title": "Log abundance in numerical dimension one for threefolds in positive characteristic", "pdf": "preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf", "folder": "preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026", "abstract_original": "We prove the numerical-dimension-one case of log abundance for threefolds over algebraically closed fields of characteristic p > 3. If $`(X,B)`$ is a projective log canonical threefold pair with effective rational boundary, and $`K_X+B`$ is ℚ-Cartier, nef, and of numerical dimension one, then $`K_X+B`$ is semiample. Neither terminality nor ℚ-factoriality of X is required.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 999, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "0938366c005f8930975b5a6633517cd5a50fe196c0fd3b58b0debc21c83b5277", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "035-02", "group": "035", "title": "Abundance in numerical dimension one for terminal threefolds in positive characteristic", "pdf": "preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf", "folder": "preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026", "abstract_original": "Let X be a projective ℚ-factorial terminal threefold over an algebraically closed field of characteristic p > 3. We prove the numerical-dimension-one case of abundance: if K X is nef with $`\\nu(K_X)=1`$, then K X is semiample and $`\\kappa(X,K_X)=1`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1008, "coverage": "catalog_only", "read_detail": null, "pages": 46, "sha256": "5e170f2c29b7026e53d167ee18a5fde3f6102de99b5e1484cd4633d03f73e26e", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "036-01", "group": "036", "title": "Numerical semiampleness of nef adjoint classes on compact Kähler manifolds", "pdf": "preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf", "folder": "preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026", "abstract_original": "Let X be a smooth connected compact Kähler manifold, let B be an effective rational simple normal crossing divisor with coefficients less than one, and let M be a nef rational holomorphic line bundle on X . If $`K_X+B`$ is pseudo-effective and $`K_X+B+M`$ is nef, we prove that its first Chern class in real Bott–Chern cohomology is represented by a semiample rational line bundle. This numerical statement allows a flat change of line bundle; it does not assert semiampleness of the original adjoint.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1024, "coverage": "catalog_only", "read_detail": null, "pages": 52, "sha256": "2f19b2f37c05dcf943a3ef1b859cb71c9e6692ca9bb0f794590ac6bd16a6ca88", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "036-02", "group": "036", "title": "Numerical Semiampleness of Nef Adjoint Divisors", "pdf": "preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf", "folder": "preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026", "abstract_original": "We prove the Generalised Abundance Conjecture: if $`(X,B)`$ is a projective klt ℚ-pair over an algebraically closed field of characteristic zero, $`K_X+B`$ is pseudo-effective, M is a nef ℚ-Cartier divisor on X , and $`K_X+B+M`$ is nef, then $`K_X+B+M`$ is numerically equivalent to a semiample ℚ-Cartier divisor on X .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1033, "coverage": "catalog_only", "read_detail": null, "pages": 37, "sha256": "b3f337e5dc5b1eda3afe298c6b97ff5eade266947e89021accfb331a3c9048c3", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "036-03", "group": "036", "title": "Minimal models and Mori fibre spaces for generalized log canonical Q-pairs", "pdf": "preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf", "folder": "preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026", "abstract_original": "We resolve the existence form of the minimal-model conjecture for projective generalized log canonical ℚ-pairs over algebraically closed fields of characteristic zero. Such a pair admits a minimal model when its adjoint divisor is pseudo-effective, and a Mori fibre space otherwise, while keeping the nef ℚ-Cartier b-divisor fixed. Taking the nef part to be zero gives the corresponding result for ordinary log canonical ℚ-pairs.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1042, "coverage": "catalog_only", "read_detail": null, "pages": 79, "sha256": "37e6d650c989c3fb3316987648aff5865f1615323274b50e5bea4794155bd22f", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "036-04", "group": "036", "title": "Minimal models in numerical dimension one", "pdf": "preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf", "folder": "preprints/Minimal-models-in-numerical-dimension-one-September-24-2026", "abstract_original": "We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If K X is pseudo-effective and $`\\kappa_\\sigma(X,K_X)=1`$, with κ σ defined by section growth with a fixed ample twist, then X admits a projective ℚ-factorial terminal minimal model.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1051, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "6fe4b337ba8c912889b0495f65c298d03abbee61c1f1641bd5a99113adf8b624", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "037-01", "group": "037", "title": "The ordinary-double-point gap in every dimension", "pdf": "preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf", "folder": "preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026", "abstract_original": "We prove the ordinary-double-point gap conjecture for boundary-zero complex algebraic klt germs in every dimension: a singular n -dimensional germ has normalized volume at most $`2(n-1)^n`$, with equality precisely at an analytic ordinary double point.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1067, "coverage": "catalog_only", "read_detail": null, "pages": 57, "sha256": "5e2cdac4857afef7065967c49c6f4f9a1aec01b0b776ce324220707545e8e114", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "037-02", "group": "037", "title": "The normalized-volume gap in dimension four", "pdf": "preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf", "folder": "preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1076, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "6d58101115e4bf4f963ea2bc4e301f041eaff601e3b325ec475200e43e3031a4", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-normalized-volume-gap-in-dimension-four-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "038-01", "group": "038", "title": "Fujita's freeness conjecture", "pdf": "preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf", "folder": "preprints/Fujitas-freeness-conjecture-September-23-2026", "abstract_original": "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 $`m\\geq n+1`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1092, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "73aefa0b0e5578dfba86cca2231608f2ba628519238cad062e49b3dc095be40b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "039-01", "group": "039", "title": "Nagata's conjecture for plane curves", "pdf": "preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf", "folder": "preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1108, "coverage": "catalog_only", "read_detail": null, "pages": 24, "sha256": "42a8897d121e2fc0bff7fe5582ea60b4b2304d706658293fb380166f46c56879", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "039-02", "group": "039", "title": "Maximal Seshadri constants on arbitrary polarized surfaces", "pdf": "preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf", "folder": "preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1117, "coverage": "catalog_only", "read_detail": null, "pages": 19, "sha256": "85976b9c9ccf5e561ae597a409f149949e2380c0e8db7e1afaa0c73ffcaf923e", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "039-03", "group": "039", "title": "Maximal Multipoint Seshadri Constants in Higher Dimensions", "pdf": "preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf", "folder": "preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026", "abstract_original": "Let L be an ample line bundle on a smooth integral complex projective variety X of dimension n ≥ 3. We prove that there is a threshold $`r_0=r_0(X,L)`$ such that for every integer $`r\\ge r_0`$, the ordinary multipoint Seshadri constant at r very general points equals the volume bound $`(L^n/r)^{1/n}`$. This establishes the qualitative Nagata–Biran–Szemberg assertion in these dimensions.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1126, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "dc7a580f2b1d6cf6b62646bbee59e3b6a9f69628c0a23c9bff0452b6a2199997", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "039-04", "group": "039", "title": "Maximal multipoint Seshadri constants in positive characteristic", "pdf": "preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf", "folder": "preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026", "abstract_original": "Let L be an ample line bundle on a smooth integral projective variety X over an algebraically closed field of positive characteristic, with $`\\dim X=n\\ge3`$. We prove that there is a threshold $`r_0=r_0(X,L)`$ such that for every integer $`r\\ge r_0`$, the ordinary multipoint Seshadri constant at the geometric generic tuple of r points equals the volume bound $`(L^n/r)^{1/n}`$. The same conclusion holds in dimension two. This establishes the positive-characteristic form of the qualitative Nagata–Biran–Szemberg assertion at geometric generic tuples.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1135, "coverage": "catalog_only", "read_detail": null, "pages": 17, "sha256": "ea4f7179e981b2729204526afa77a0262ba3130eb2d92dcbfccfca234ddc0ae4", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "040-01", "group": "040", "title": "Bloch’s conjecture for surfaces with p_g=0", "pdf": "preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf", "folder": "preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026", "abstract_original": "We prove Bloch's conjecture for smooth connected projective complex surfaces with $`p_g=0`$: the Albanese homomorphism on integral degree-zero zero-cycles is an isomorphism.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1151, "coverage": "catalog_only", "read_detail": null, "pages": 45, "sha256": "afb7bf56f8d97111983646a0791ef45c85cfa64dbc1fb3b2ebd7cff24170a0aa", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "041-01", "group": "041", "title": "Projective-space bases of Lagrangian fibrations", "pdf": "preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf", "folder": "preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026", "abstract_original": "We prove that the normal projective base of a projective Lagrangian fibration from a compact irreducible holomorphic symplectic Kähler manifold is projective space. This resolves the projective-space base conjecture for such fibrations in every dimension and deformation type.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1167, "coverage": "catalog_only", "read_detail": null, "pages": 98, "sha256": "5fdf543649f1469a097badf9e3cb603031110f8dff1dbacb85f49fcbc99c125d", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "041-02", "group": "041", "title": "The strong hyperkähler SYZ conjecture", "pdf": "preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf", "folder": "preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1176, "coverage": "catalog_only", "read_detail": null, "pages": 32, "sha256": "dbb30c29398fcfa0905ac92b97a11fbfd5a56f1861fb88ae1a50c8137ac601eb", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "042-01", "group": "042", "title": "Every complex K3 surface is Oka", "pdf": "preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf", "folder": "preprints/Every-complex-K3-surface-is-Oka-September-23-2026", "abstract_original": "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 ℂ m can be approximated uniformly on that set by entire maps $`\\mathbb C^m\\to X`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1192, "coverage": "catalog_only", "read_detail": null, "pages": 56, "sha256": "c35e20c01dcefe7634db141846045e88676001de7097c3678832b322ecbd9734", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "043-01", "group": "043", "title": "P=W in composite rank for fixed determinant", "pdf": "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", "folder": "preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1208, "coverage": "catalog_only", "read_detail": null, "pages": 39, "sha256": "52c828f91521d93c3fe4dab01c3c1d8bdaa580c1470834711c6d97f1d73c1193", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/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", "online_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", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "044-01", "group": "044", "title": "The equivariant cohomological Hikita conjecture for arbitrary quivers", "pdf": "preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf", "folder": "preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1224, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "9f66ad939e0e51ecbe116ea72084ecef9f1121c6fea1cc733c7dde6d70b3e47b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "046-01", "group": "046", "title": "A projective fourfold with large fundamental group and non-Stein universal cover", "pdf": "preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf", "folder": "preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026", "abstract_original": "We construct a smooth projective complex fourfold with large fundamental group whose universal cover is not Stein. The universal cover contains no positive-dimensional compact complex-analytic subvariety, so this disproves Shafarevich's holomorphic-convexity conjecture even under the large-fundamental-group hypothesis.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1240, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "bb2a84e535643f767166d6b2918821d3de18dbff884958cdcc6100f15d1e64a7", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "046-02", "group": "046", "title": "A surface counterexample to Shafarevich holomorphic convexity", "pdf": "preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf", "folder": "preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1249, "coverage": "catalog_only", "read_detail": null, "pages": 26, "sha256": "d99ed633f092375c6b34a026df5d81c56ef9da8b99ca8e9f990146078b71a66a", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "047-01", "group": "047", "title": "An explicit failure of complex affine-space cancellation", "pdf": "preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf", "folder": "preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026", "abstract_original": "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 𝔸 3 -fibrations over 𝔸 1 and 𝔸 2 that are not Zariski-locally trivial. These fibrations disprove the Dolgachev–Weisfeiler affine-fibration conjecture over these bases.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1265, "coverage": "catalog_only", "read_detail": null, "pages": 29, "sha256": "91a1a2f28c960cba25dd268e0f5515f0cff31463e4342098bbd89f857dd82023", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "048-01", "group": "048", "title": "A singular normal affine surface with free tangent sheaf", "pdf": "preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf", "folder": "preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026", "abstract_original": "We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1281, "coverage": "catalog_only", "read_detail": null, "pages": 37, "sha256": "48b1a74d3131e97b2cb8ed8f5c1d29458e8f2e92b6446d5d9d0161c4ab3612db", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "049-01", "group": "049", "title": "A stable coordinate that is not a coordinate in four variables", "pdf": "preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf", "folder": "preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026", "abstract_original": "We construct an explicit degree-five polynomial over $`\\mathbf C`$ that is not a coordinate in four variables but becomes one after adjoining a single variable. This gives a counterexample to the stable coordinate conjecture in four variables. Every fiber is isomorphic to affine three-space, yet its embedding in affine four-space is not rectifiable. Thus the example also disproves the Abhyankar–Sathaye embedding conjecture in ambient dimension four.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1297, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "52d49d150cf01ef08c0eb878d1fde75b17125437a276a9616b4df7f1adeedcaa", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "049-02", "group": "049", "title": "An explicit noncoordinate polynomial with affine three-space zero fibre", "pdf": "preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf", "folder": "preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026", "abstract_original": "We construct an explicit counterexample to the Abhyankar–Sathaye conjecture: a noncoordinate polynomial in four complex variables whose zero fibre is affine three-space. Adjoining variables gives counterexamples in every ambient dimension at least four.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1306, "coverage": "catalog_only", "read_detail": null, "pages": 6, "sha256": "a0f2145ec95a6083a4a9a54ef4d2c41fa9587cd435c6908c512ce90e6c64154b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "050-01", "group": "050", "title": "Ample rank-two bundles on the quadric surface without Griffiths-positive metrics", "pdf": "preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf", "folder": "preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1322, "coverage": "catalog_only", "read_detail": null, "pages": 18, "sha256": "af1c052828ec09138c76a64edeed05edd429e4634bf61a4fecdda9d86fd1eb9b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf", "online_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", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "051-01", "group": "051", "title": "Canonical ampleness of compact hyperbolic Kähler manifolds", "pdf": "preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf", "folder": "preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1338, "coverage": "catalog_only", "read_detail": null, "pages": 31, "sha256": "146466e3aa616985072493a7d0beb88514c122fccee9be5b7287cd6c75d36415", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "052-01", "group": "052", "title": "Universal-cover splitting for compact Kähler manifolds", "pdf": "preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf", "folder": "preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026", "abstract_original": "We prove the two-summand form of Beauville's compatible splitting conjecture. If the tangent bundle of a compact connected Kähler manifold decomposes into two integrable holomorphic subbundles of positive rank, then its ordinary universal cover admits a product decomposition whose factor tangent bundles are the lifted specified summands.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1354, "coverage": "catalog_only", "read_detail": null, "pages": 33, "sha256": "14d3e3f23539fd98735adb5042214f7f6eac9499a47e3303018932e00d29d333", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "052-02", "group": "052", "title": "Integrability of split tangent bundles on rationally connected manifolds", "pdf": "preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf", "folder": "preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1363, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "cb23bde917710f73321f4342b88dba8135aeb84b4c553f57df7d5532de73c01d", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "053-01", "group": "053", "title": "A high-arity counterexample to Pixton completeness in Chow", "pdf": "preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf", "folder": "preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026", "abstract_original": "We disprove the Chow and rational-cohomological forms of Pixton's completeness conjecture for his original relation system. We construct a formal tautological class outside the original Pixton relation span whose image is zero in the Chow ring and in rational cohomology. The example has genus $`10^{60}`$ and $`3\\binom{10^{60}}3`$ markings.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1379, "coverage": "catalog_only", "read_detail": null, "pages": 61, "sha256": "e52ae0e71ab4c7b5edb9bf47269fc79c674a93161bb1709920990dceccf33a53", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "054-01", "group": "054", "title": "Irrational cubic fourfolds with geometric K3 categories", "pdf": "preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf", "folder": "preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1395, "coverage": "catalog_only", "read_detail": null, "pages": 62, "sha256": "4f870a96114f1ac89a5fe55b4eb13f17a2690446f82ff28aa7829199a7832952", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf", "online_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", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "055-01", "group": "055", "title": "A Gepner stability condition on every smooth quintic threefold", "pdf": "preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026/paper.pdf", "folder": "preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026", "abstract_original": "We prove Toda's normalized quintic Gepner conjecture. On every smooth complex quintic threefold, we construct a numerical Bridgeland stability condition for which tensoring by the hyperplane bundle, followed by the spherical twist at the structure sheaf, increases phase by 2/5.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1411, "coverage": "catalog_only", "read_detail": null, "pages": 22, "sha256": "f70b73596fffb0689874c768d3975cb8e16cbdede231c21baef0707ab1898f49", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Gepner-stability-condition-on-every-smooth-quintic-threefold-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "055-02", "group": "055", "title": "Prescribed large-volume charges on threefolds with trivial canonical bundle", "pdf": "preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026/paper.pdf", "folder": "preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026", "abstract_original": "Let X be a smooth projective complex threefold with trivial canonical bundle. We construct numerical Bridgeland stability conditions with the exact ordinary and square-root-Todd central charges at every sufficiently large volume. One volume threshold works on an open set of real twists and ample directions. The resulting stability conditions have the support property on the full numerical Grothendieck group and stable point sheaves. Separately, on every smooth projective complex threefold we prove a strong tilt inequality above a volume threshold uniform in the object and twist along a fixed polarization.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1420, "coverage": "catalog_only", "read_detail": null, "pages": 49, "sha256": "84ce978a670157043e5a8bc24583d2eb290cecf379a9f1ec495b6084e8c3f3f2", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "056-01", "group": "056", "title": "Termination of generalized log canonical flips on compact Kähler fourfolds", "pdf": "preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf", "folder": "preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026", "abstract_original": "Every sequence of generalized log canonical flips on a normal irreducible globally Weil ℚ-factorial compact Kähler fourfold terminates, provided the flips are projective small diagrams with the stated opposite ample signs. The boundary is rational, and the nef b-divisor is fixed and represented by an analytically nef ℚ-Cartier divisor on a projective modification. No scaling rule or pseudo-effectivity assumption is required. The theorem concerns existing flip sequences; it does not assert the existence of all contractions or flips.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1436, "coverage": "catalog_only", "read_detail": null, "pages": 47, "sha256": "e0e35c0328f2caef0bdbfcdc30347da8c78e209515ff5bd112114ceed51a9e97", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "056-02", "group": "056", "title": "Termination of generalized-canonical flips on compact Kähler fourfolds", "pdf": "preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf", "folder": "preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026", "abstract_original": "Every sequence of generalized-canonical flips on compact Kähler fourfolds with rational boundary and fixed rational analytically nef b-divisor terminates when the small morphisms are projective. We prove this for normal globally Weil ℚ-factorial models with boundary coefficients less than one, allowing exceptional log discrepancies equal to one. No scaling rule or pseudo-effectivity assumption is required. The theorem applies to existing projective small diagrams with the specified opposite ample signs.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1445, "coverage": "catalog_only", "read_detail": null, "pages": 22, "sha256": "6f647b4844ccefe7352ae5883e8a727c13bbd545b5df68a385852b669d55dadd", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "056-03", "group": "056", "title": "Termination for projective log canonical fourfolds with rational boundary", "pdf": "preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf", "folder": "preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026", "abstract_original": "We prove that every permitted minimal model program for a projective log canonical fourfold with rational boundary over an algebraically closed field of characteristic zero terminates. The result allows arbitrary negative extremal rays and mixed birational steps on the given models, without pseudo-effectivity or initial ℚ-factoriality.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1454, "coverage": "catalog_only", "read_detail": null, "pages": 44, "sha256": "8ac06a1f5c9a11c5b22ebdae27dd2c0b51d966e0aed19996713f7acafe737f0a", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "056-04", "group": "056", "title": "Finite ordinary minimal model programs on compact Kähler fourfolds", "pdf": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "folder": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026", "abstract_original": "We prove that every maximal ordinary negative-ray program starting from a compact Kähler klt fourfold pair with effective rational boundary in the global Weil-divisor ℚ-factorial category terminates. It ends at a nef model when the adjoint is pseudo-effective and at a projective Mori fibre space otherwise.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1463, "coverage": "catalog_only", "read_detail": null, "pages": 89, "sha256": "b1b9511572d6c717db55176347c5fdb90013f93df7b20fa95dd8801c86b19172", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "056-05", "group": "056", "title": "Finite ordinary minimal model programs on compact Kähler fourfolds", "pdf": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf", "folder": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026", "abstract_original": "We prove that a globally Weil-ℚ-factorial compact Kähler klt fourfold pair with effective rational boundary and canonical rational line bundle admits a finite ordinary minimal model program starting on the given pair. It ends at a nef model when the adjoint class is pseudo-effective and at a Mori fibre space otherwise.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1472, "coverage": "catalog_only", "read_detail": null, "pages": 35, "sha256": "4aa0d0c5f7298f8e05371abf686297181c82df885d316bf96073bb47641dbe12", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "057-01", "group": "057", "title": "The abelianity conjecture for special compact Kähler manifolds", "pdf": "preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf", "folder": "preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1488, "coverage": "catalog_only", "read_detail": null, "pages": 50, "sha256": "dfbf9ad2335b9d20dedd8a2ae527ebb45b74155a976acc6d284dd851144e22b8", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-abelianity-conjecture-for-special-compact-Kahler-manifolds-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "057-02", "group": "057", "title": "Two-step monodromy of special quasi-projective varieties", "pdf": "preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026/paper.pdf", "folder": "preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026", "abstract_original": "We give an independent proof that every complex linear representation of the ordinary fundamental group of a connected smooth special complex quasi-projective variety has virtually nilpotent image of class at most two. This conclusion was previously announced by Cao–Deng–Hacon–Păun. We also construct special open surfaces whose general quasi-Albanese fibres are not special.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1497, "coverage": "catalog_only", "read_detail": null, "pages": 19, "sha256": "dbc966a951e13d2e0a3184321968aa7c569d102c90759e1868024cdf8734cbe4", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Two-step-monodromy-of-special-quasi-projective-varieties-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "057-03", "group": "057", "title": "A conditional abelianity theorem for special fourfold pairs with a half-weight divisor", "pdf": "preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf", "folder": "preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026", "abstract_original": "Using the abelianity theorem for special compact Kähler manifolds in every dimension, we prove virtual abelianity of the entire orbifold fundamental group of the special order-two root orbifold associated with a pair $`(X,\\tfrac12D)`$, where X is a smooth projective fourfold and D is a nonempty smooth connected divisor. We construct a special smooth projective eightfold whose fundamental group surjects onto the required group.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1506, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "d017fae040e20002b012b8636d9a757cb4471728d3e06d6b80cca60970602c32", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "058-01", "group": "058", "title": "Semialgebraic universal covers of normal projective varieties", "pdf": "preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf", "folder": "preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1522, "coverage": "catalog_only", "read_detail": null, "pages": 65, "sha256": "dd294523779a9237a2ae4d5399e874bdfbfddbfe8c54a379240aeb2d2c75bf1b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Semialgebraic-universal-covers-of-normal-projective-varieties-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "058-02", "group": "058", "title": "Symmetry of semialgebraic bounded domains with compact quotient", "pdf": "preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf", "folder": "preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1531, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "a93c6ca7f3221b4598a22cac0b0b313a2661c5d8be148b8f274b04efcb42045d", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "059-01", "group": "059", "title": "Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three", "pdf": "preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026/paper.pdf", "folder": "preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026", "abstract_original": "We give a negative answer to the embedded Zariski multiplicity conjecture. We construct two reduced hypersurface germs that are ambiently homeomorphic but have multiplicities two and three. Both have isolated singularities and lie in a common complex affine space of dimension divisible by eight. Their defining function germs are also topologically right equivalent, and the same examples answer Arnold's corank problem negatively for ambient topological equivalence.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1547, "coverage": "catalog_only", "read_detail": null, "pages": 31, "sha256": "ce7e450c32aa20ca778333f1b7fc2ec0df51041f8fc6dd78e4d48d1f5de1b73d", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Ambiently-homeomorphic-isolated-hypersurfaces-of-multiplicities-two-and-three-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "059-02", "group": "059", "title": "Ambiently homeomorphic isolated hypersurface germs in ℂ⁴ with multiplicities four and five", "pdf": "preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf", "folder": "preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026", "abstract_original": "We give a negative answer to Zariski's multiplicity question in four complex variables. We construct two reduced convergent holomorphic function germs with isolated critical points and multiplicities four and five whose zero-set germs are ambiently homeomorphic.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1556, "coverage": "catalog_only", "read_detail": null, "pages": 32, "sha256": "7b9c31dcfb1ba9b7c68b7ec31829963eebffcd6171a8139c26c20ee6c60e3b16", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "060-01", "group": "060", "title": "Global Spherical Shells on Minimal Surfaces of Class VII", "pdf": "preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf", "folder": "preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026", "abstract_original": "We prove the Global Spherical Shell conjecture: every connected minimal compact complex surface of class VII with positive second Betti number contains a global spherical shell. This is a holomorphically embedded neighborhood of the standard three-sphere in $`\\mathbb C^2\\setminus\\{0\\}`$ whose complement is connected.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1572, "coverage": "catalog_only", "read_detail": null, "pages": 39, "sha256": "d441e45f773bce9fc3728c7de5f2cfb21fcb92849c9e8403561a787c335f4aae", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "062-01", "group": "062", "title": "Contact Fano manifolds and the LeBrun–Salamon conjecture", "pdf": "preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf", "folder": "preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1588, "coverage": "catalog_only", "read_detail": null, "pages": 40, "sha256": "c7ef1ec44ffd8d7aa71952e4a231d60a449a5f9f2ad18fcfa897df888b829e7c", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "063-01", "group": "063", "title": "The generalized Mukai conjecture", "pdf": "preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf", "folder": "preprints/The-Generalized-Mukai-Conjecture-September-24-2026", "abstract_original": "We prove the generalized Mukai conjecture: every positive-dimensional smooth complex Fano manifold of dimension n , Picard number ρ , and pseudoindex ι satisfies $`\\rho(\\iota-1)\\le n`$. Equality holds precisely for the product of ρ copies of $`\\mathbb P^{\\iota-1}`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1604, "coverage": "catalog_only", "read_detail": null, "pages": 19, "sha256": "0273a9c7907eb9d1ab3b3f99ff5668503c4db51764545764e91b03389e267317", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "064-01", "group": "064", "title": "Topological triviality of mu-constant families of surface singularities", "pdf": "preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf", "folder": "preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026", "abstract_original": "We prove that every holomorphic one-parameter family of isolated hypersurface singularities in ℂ 3 with constant Milnor number is topologically right-trivial. This gives a positive answer to the surface case of the μ -constant problem. The trivialization fixes the parameter and the origin section, and preserves the defining functions.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1620, "coverage": "catalog_only", "read_detail": null, "pages": 37, "sha256": "133a57483691850c2e22906e53e0b662047c1d6caf262418ac509d6b4fd1a928", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "065-01", "group": "065", "title": "Virasoro Constraints under Projectivization", "pdf": "preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf", "folder": "preprints/Virasoro-Constraints-under-Projectivization-October-5-2026", "abstract_original": "We prove that full ordinary descendant Virasoro constraints pass from a smooth projective complex base to the projectivization of any algebraic vector bundle of rank at least two. The bundle need not split and satisfies no positivity requirement. Assuming the full constraints on the base, the conclusion includes every genus, each individual integral curve class, and all cohomology insertions, including primitive and odd classes. The result also applies successively to towers of projective bundles.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1636, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "573917aea43c708a8cbef22a209158e5d6ea0e9d71f7786967608483be4709e6", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "065-02", "group": "065", "title": "Virasoro Constraints for Projective Complete Intersections", "pdf": "preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf", "folder": "preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1645, "coverage": "catalog_only", "read_detail": null, "pages": 48, "sha256": "01a2df978a0bfae2ae243765734233ef1d98f825a2f0e26736b01c993c0544ca", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "066-01", "group": "066", "title": "Bounded klt complements for Fano contractions", "pdf": "preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf", "folder": "preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026", "abstract_original": "For fixed dimension d and positive rational ϵ , we prove that every ϵ -log-canonical Fano contraction over an algebraically closed field of characteristic zero admits, near each closed base point, a klt complement of index bounded only by d and ϵ . Over ℂ, we also obtain monotone klt complements for Fano type pairs with nef anti-log-canonical divisor and coefficients in a fixed finite rational set. This proves the finite-rational-coefficient form of Shokurov's bounded-klt-complement conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1661, "coverage": "catalog_only", "read_detail": null, "pages": 93, "sha256": "d50937326c7cb11549cc75d8daf5cd57656f85cf52f52a7cf551c22104482c67", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "066-02", "group": "066", "title": "Uniform Cartier sections for Fano type contractions", "pdf": "preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf", "folder": "preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026", "abstract_original": "We prove the Cartier-divisor conjecture of Birkar and Shokurov for rational boundaries in characteristic zero and for real boundaries over ℂ. For an ϵ -lc Fano type contraction with positive-dimensional base and nef negative log canonical class, a Cartier divisor through any prescribed base point can be chosen with pullback log canonical threshold bounded below in terms of the dimension and ϵ alone.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1670, "coverage": "catalog_only", "read_detail": null, "pages": 106, "sha256": "8d97ba60373419ba60890f3a130a854481596ac206dc2902f299ac542e4f761b", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026/Uniform-Cartier-sections-for-Fano-type-contractions-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "067-01", "group": "067", "title": "The Campana–Peternell conjecture in dimension six", "pdf": "preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf", "folder": "preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026", "abstract_original": "We prove that every smooth connected complex projective Fano sixfold with nef tangent bundle is rational homogeneous, resolving the Campana–Peternell conjecture in complex dimension six. As a consequence, a connected compact Kähler manifold X with nef holomorphic tangent bundle and $`\\dim_{\\mathbb C}X-\\widetilde q(X)\\leq6`$ has ordinary universal cover $`F\\times\\mathbb C^{\\widetilde q(X)}`$, where F is a rational homogeneous manifold and $`\\widetilde q(X)`$ is the maximal irregularity of a connected finite étale cover.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1686, "coverage": "catalog_only", "read_detail": null, "pages": 27, "sha256": "c6c7151f9581ddd5b4d4bea3e6c1e96bf1fa776b97f6e0f2e2de1b952d5a28a1", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-01", "group": "068", "title": "Anticanonical nonvanishing from smooth semipositivity", "pdf": "preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf", "folder": "preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026", "abstract_original": "Every smooth connected projective complex variety with smoothly semipositive anticanonical bundle has a nonzero section of some positive anticanonical power.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1702, "coverage": "catalog_only", "read_detail": null, "pages": 27, "sha256": "ff5a08aaa3d9ad2315fa2e8afac88e60f1764b27b17609ee321a4a3d0e14b796", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-02", "group": "068", "title": "Invariant anticanonical indices and conversion of twisted differentials", "pdf": "preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf", "folder": "preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026", "abstract_original": "For a holomorphic action of a compact torus on a compact complex manifold, we prove that the invariant Euler characteristic of naturally linearized anticanonical powers is polynomial on a divisible progression, with its actual value at exponent zero. Independently, on a smooth projective variety with smoothly semipositive anticanonical bundle, we remove a fixed pseudoeffective error from an unbounded sequence of effective twists. These results convert invariant cohomology into twisted differential forms and prove anticanonical nonvanishing on smooth projective varieties with smoothly semipositive anticanonical bundle, by descending the forms before conversion.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1711, "coverage": "catalog_only", "read_detail": null, "pages": 18, "sha256": "c40b47629aa1aa95cbb7b6f5d4bd9d4b14ef61616326923c36a17e1f4759599f", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-03", "group": "068", "title": "Bounded anticanonical metrics on klt pairs and torus quotients", "pdf": "preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026/main.pdf", "folder": "preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026", "abstract_original": "Let $`(W,D)`$ be a projective ℚ-factorial klt pair with effective rational boundary. We prove that a positive Cartier multiple of $`-(K_W+D)`$ has a nonzero section if this divisor is nef, its pullback to a resolution admits a semipositive metric with locally bounded weights, and the resolution has nonzero structure-sheaf Euler characteristic. Consequently a smooth rationally connected projective variety with smoothly semipositive anticanonical bundle has a nonzero naturally invariant anticanonical plurisection for every algebraic torus action.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1720, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "2420934378c18da636bae46c45903c4029b88121cebe88a8402117e148838d64", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Bounded-anticanonical-metrics-on-klt-pairs-and-torus-quotients-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-04", "group": "068", "title": "Cohomological transfer and equivariant anticanonical sections", "pdf": "preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026/main.pdf", "folder": "preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026", "abstract_original": "Let X be a smooth projective complex variety with smoothly semipositive anticanonical bundle. For any torus linearization of that bundle, we show that invariant sections in unbounded degrees with one fixed negative pseudoeffective error yield an invariant section in a positive untwisted degree. Combining the natural invariant index with compact-monodromy structure, we deduce that every such X has a nonzero section of some positive anticanonical power.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1729, "coverage": "catalog_only", "read_detail": null, "pages": 43, "sha256": "6e231fa726d0f6b62052823b6f57488108d352d56c326c3aad1cd59a126fc53c", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Cohomological-transfer-and-equivariant-anticanonical-sections-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-06", "group": "068", "title": "Integrable metrics and effectivity with controlled boundary", "pdf": "preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf", "folder": "preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026", "abstract_original": "Let Y be smooth projective and let C be an effective integral divisor. If $`-K_Y+C`$ admits a metric with a global strict curvature lower bound for which the canonical section of C is locally square integrable, every pseudoeffective rational divisor becomes rationally effective after an effective correction supported on C . For a smooth projective X with smoothly semipositive $`L=-K_X`$, sections of $`m_jL-P`$ at unbounded positive exponents, with any fixed pseudoeffective Cartier error P , yield a section of a positive multiple of L .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1747, "coverage": "catalog_only", "read_detail": null, "pages": 45, "sha256": "79cff3abcc899987e13e6669facada18a66322a0b10b9453e5568088ec5537d4", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "068-07", "group": "068", "title": "Exact orders and invariant anticanonical linear systems", "pdf": "preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026/main.pdf", "folder": "preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026", "abstract_original": "On a smooth connected projective complex variety with smoothly semipositive anticanonical bundle, we prove that asymptotically zero valuation on the curvature-null face is attained by an effective rational anticanonical divisor. The fixed auxiliary line bundle is arbitrary.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 1756, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "f93f24f5a8ef95cfb95fd1e52a4315e43cc3931c13ebaf1c2c25330013427dd0", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Exact-orders-and-invariant-anticanonical-linear-systems-September-26-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "193-01", "group": "193", "title": "Positivity of Serre's Intersection Multiplicity", "pdf": "preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf", "folder": "preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4434, "coverage": "catalog_only", "read_detail": null, "pages": 31, "sha256": "7985cfbc11547cf659efdd6abc076a0c0371e9a38e8026aa09b23cbb042af917", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "194-01", "group": "194", "title": "Lech's multiplicity conjecture", "pdf": "preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf", "folder": "preprints/Lechs-multiplicity-conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4450, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "1fbf2cdd8ba384fa9d711c68746b0114240b37cafc56a27e32bac52f179d3e31", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "195-01", "group": "195", "title": "A Complete Local Domain without a Small Cohen–Macaulay Module", "pdf": "preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf", "folder": "preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026", "abstract_original": "We construct a three-dimensional complete Noetherian normal local domain containing ℂ, with residue field ℂ, that has no nonzero finitely generated maximal Cohen–Macaulay module. This disproves the domain form of the small Cohen–Macaulay module conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4466, "coverage": "catalog_only", "read_detail": null, "pages": 17, "sha256": "370f49638a5305de053dac3dc3a82a6757cc49efb70a3e2d80912cbf3ca0ed2f", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Complete-Local-Domain-Without-a-Small-Cohen-Macaulay-Module-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "196-01", "group": "196", "title": "A Torsion-Free Group Algebra with Zero Divisors", "pdf": "preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf", "folder": "preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4482, "coverage": "catalog_only", "read_detail": null, "pages": 26, "sha256": "b9788d4579b317fa2487796338fe3413322e105950880ec5a42bc85188a36bc6", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "197-01", "group": "197", "title": "A Torsion-Free Group Algebra That Is Not Directly Finite", "pdf": "preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf", "folder": "preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026", "abstract_original": "We construct a finitely presented torsion-free counterexample to Kaplansky's direct finiteness conjecture over the field of two elements. The group admits a finite two-dimensional classifying complex.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4498, "coverage": "catalog_only", "read_detail": null, "pages": 31, "sha256": "7950476863f21811aaccb99ab12f24f81741e5077ca290394d029063024aaee8", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Group-Algebra-That-Is-Not-Directly-Finite-October-4-2026/direct-finiteness.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "197-02", "group": "197", "title": "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Characteristic Two", "pdf": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf", "folder": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026", "abstract_original": "We disprove Kaplansky's direct-finiteness conjecture by constructing a finite field K of characteristic two, a finitely presented group G , and finite sums $`a,b\\in K[G]`$ with $`ab=1`$ but $`ba\\ne1`$. The group G is nonsofic. The same elements define a cellular automaton on K G that is injective but not surjective, disproving Gottschalk's surjunctivity conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4507, "coverage": "catalog_only", "read_detail": null, "pages": 28, "sha256": "a97d7915d43b5112b11b7ae39619cf3a7b9c40f207f8f586fc28f22ff4406d12", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Characteristic-Two-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "197-03", "group": "197", "title": "A Counterexample to the Group-Ring Determinant Conjecture", "pdf": "preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf", "folder": "preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4516, "coverage": "catalog_only", "read_detail": null, "pages": 9, "sha256": "3524b6f2390f17d5af1f06d76bfa0a6560cbdc3cb6d1d316fcdf17a715d0de40", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-the-Group-Ring-Determinant-Conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "197-04", "group": "197", "title": "A Counterexample to Kaplansky's Direct-Finiteness Conjecture in Odd Characteristic", "pdf": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf", "folder": "preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026", "abstract_original": "We construct a counterexample to Kaplansky's direct-finiteness conjecture in odd characteristic. For one specified odd prime p , we obtain a field K of order p 4 , a finitely generated group G containing torsion, and finite sums $`a,b\\in K[G]`$ with $`ab=1`$ but $`ba\\ne1`$. The same elements define a cellular automaton on K G that is injective but not surjective.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4525, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "dc312586744d8d1b4fe49672ee36323fd56328f7ff3b9d8a481ddfb12b6965fe", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kaplanskys-Direct-Finiteness-Conjecture-in-Odd-Characteristic-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "198-01", "group": "198", "title": "An algebra of infinite little finitistic dimension", "pdf": "preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf", "folder": "preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026", "abstract_original": "We construct a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4541, "coverage": "catalog_only", "read_detail": null, "pages": 24, "sha256": "1fb7f827f59dcca0f391c279c346e4e8bc941880c24ec30fe1cba2e9a319f89c", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "199-01", "group": "199", "title": "An explicit counterexample to the Auslander-Reiten conjecture", "pdf": "preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf", "folder": "preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026", "abstract_original": "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 .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4557, "coverage": "catalog_only", "read_detail": null, "pages": 30, "sha256": "22f6a9d5151fca3a323b9a1b91f6eb3ccf4c84cde00e9dfdeccb760a380ed6c3", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-explicit-counterexample-to-the-Auslander-Reiten-conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "199-02", "group": "199", "title": "A counterexample to Tachikawa's second conjecture", "pdf": "preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf", "folder": "preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026", "abstract_original": "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 .", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4566, "coverage": "catalog_only", "read_detail": null, "pages": 39, "sha256": "332c2535f60d4ad620a86b3c4d547c51510b183f881445d9a0807986b0544f67", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "200-01", "group": "200", "title": "The Artinian Lex-Plus-Powers Betti Theorem", "pdf": "preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf", "folder": "preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4582, "coverage": "catalog_only", "read_detail": null, "pages": 22, "sha256": "81874e1994ff2773543f714989feac78650ddc902f7f36047c6ce8d3288a9c05", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Artinian-Lex-Plus-Powers-Betti-Theorem-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "200-02", "group": "200", "title": "Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture", "pdf": "preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf", "folder": "preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4591, "coverage": "catalog_only", "read_detail": null, "pages": 43, "sha256": "20fba09b5fed0f63cb54b9f4bc750627ac834a2ef73fcd8d41a2ea83cac56069", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf", "online_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", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "201-01", "group": "201", "title": "A Counterexample to Kurosh’s Division-Ring Problem", "pdf": "preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf", "folder": "preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4607, "coverage": "catalog_only", "read_detail": null, "pages": 45, "sha256": "9195b0a83fc633704a735973a068257d424a46196a74cad21176e49348147aec", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "202-01", "group": "202", "title": "The Blockwise Alperin Weight Conjecture", "pdf": "preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf", "folder": "preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4623, "coverage": "catalog_only", "read_detail": null, "pages": 59, "sha256": "042c7730f058d508443b2c34fd8aa4d31acf72292bcb76d14ee9f0f3068cee70", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "203-01", "group": "203", "title": "Donovan's Conjecture over Algebraically Closed Fields", "pdf": "preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf", "folder": "preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026", "abstract_original": "We prove Donovan's conjecture over every algebraically closed field K of characteristic p > 0. For each fixed K and bound on defect-group order, blocks of finite groups represent only finitely many K -linear Morita equivalence classes. The defect groups need not be abelian, and the result includes p = 2.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4639, "coverage": "catalog_only", "read_detail": null, "pages": 94, "sha256": "80d721e72d29a9bc4c10cd0341d766e3329a1fdeeb5fce3f5837049ebf66a23c", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "203-02", "group": "203", "title": "Integral Donovan Finiteness over Witt Vectors", "pdf": "preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf", "folder": "preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026", "abstract_original": "We prove integral Donovan finiteness: for every prime p and positive integer M , the blocks of all finite groups with defect groups of order at most M have only finitely many Morita equivalence classes over $`W(\\overline{\\mathbb F}_p)`$. The defect groups need not be abelian, and the result includes p = 2. The same bounded-defect finiteness holds over each fixed complete discrete valuation ring of characteristic zero with algebraically closed residue field of characteristic p , including ramified rings.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4648, "coverage": "catalog_only", "read_detail": null, "pages": 22, "sha256": "ab8478191fa023afb324800e025504e0436cc0f189cca5189203b69444ee4156", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "204-01", "group": "204", "title": "Tensor saturation for even spin groups", "pdf": "preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf", "folder": "preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026", "abstract_original": "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.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4664, "coverage": "catalog_only", "read_detail": null, "pages": 46, "sha256": "aa18cc9fdf4734cca86ca3a36d6a9be7544e29ca24e2700e0537c938b93d5be3", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf", "online_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", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "205-01", "group": "205", "title": "Universal Tensor Squares for Symmetric Groups", "pdf": "preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf", "folder": "preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026", "abstract_original": "For every positive integer n other than 2, 4, and 9, we prove that some irreducible complex representation of S n has a tensor square containing every irreducible representation. This resolves the tensor square conjecture for symmetric groups affirmatively.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4680, "coverage": "catalog_only", "read_detail": null, "pages": 37, "sha256": "822ceb3f2a80c93584712b517d6e13d4a3d96e4233a69a14720c17edc6ccc925", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "205-02", "group": "205", "title": "A Cyclic Polytabloid Proof of Saxl's Conjecture", "pdf": "preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf", "folder": "preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026", "abstract_original": "For every staircase partition, we prove that the tensor square of the corresponding irreducible complex representation of the symmetric group contains every irreducible representation of that group. This proves Saxl's conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4689, "coverage": "catalog_only", "read_detail": null, "pages": 17, "sha256": "42c2824b06a1114993095d44e1226e7f15f17caaa09358d68fa5dfddedbd8f44", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Cyclic-Polytabloid-Proof-of-Saxls-Conjecture-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "206-01", "group": "206", "title": "Finite congruence lattices: characterization and undecidability", "pdf": "preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026/paper.pdf", "folder": "preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026", "abstract_original": "We give an explicit colored-graph characterization of the finite nonempty lattices that occur as full congruence lattices of finite algebras, and prove that deciding this representation property is undecidable. In particular, the finite lattice representation problem has a negative answer. We also prove that recognition of full subgroup intervals in finite groups is undecidable.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4705, "coverage": "catalog_only", "read_detail": null, "pages": 180, "sha256": "d26d6cd6285de4f24158d37d1583bdee84a6426190e1b6df67853128e57d80f9", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Finite-Congruence-Lattices-Characterization-and-Undecidability-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "206-02", "group": "206", "title": "A negative solution to the finite lattice representation problem", "pdf": "preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf", "folder": "preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026", "abstract_original": "We give a negative solution to the finite lattice representation problem. We prove that there is a finite nonempty lattice that is not the full congruence lattice of any finite nonempty algebra of any finite signature.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4714, "coverage": "catalog_only", "read_detail": null, "pages": 87, "sha256": "a102efd4a3009423f0e36d9e73a239a57f6507cb57d3e9e3fe6d8a22208af876", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "207-01", "group": "207", "title": "The ℓ¹-Bass Conjecture for Discrete Groups", "pdf": "preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf", "folder": "preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026", "abstract_original": "We prove the ℓ 1 -Bass conjecture for every discrete group. The Hattori–Stallings trace of every idempotent matrix over the complex ℓ 1 group algebra is supported on finitely many conjugacy classes of finite-order elements.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4730, "coverage": "catalog_only", "read_detail": null, "pages": 33, "sha256": "9894680d2ffb10ff5ea369fcc9d41c7cfe63e20f09f8182dcf86c60746139797", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "207-02", "group": "207", "title": "The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture", "pdf": "preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf", "folder": "preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026", "abstract_original": "We prove the complex group-ring Bass trace conjecture for every discrete group: the Hattori–Stallings trace of a finitely generated projective module over its complex group ring is supported on conjugacy classes of finite-order elements. As a consequence, for every torsion-free group G and every commutative unital domain R of characteristic zero, the only idempotents in $`RG`$ are 0 and 1. This proves Kaplansky's idempotent conjecture in characteristic zero.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4739, "coverage": "catalog_only", "read_detail": null, "pages": 33, "sha256": "1c4d90b5ed4de2ef66b4b07b3d5c3e2bfe8822a538177c64ee1d3c3e091120bf", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026/The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "208-01", "group": "208", "title": "Fiber functors for finite symmetric tensor categories in positive characteristic", "pdf": "preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf", "folder": "preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026", "abstract_original": "We prove the finite case of the Benson–Etingof–Ostrik conjecture: every finite symmetric tensor category over an algebraically closed field k of characteristic p > 0 admits a k -linear exact faithful strong symmetric monoidal functor to a finite higher Verlinde category $`\\mathop{\\mathrm{Ver}}\\nolimits _{p^n}(k)`$. The result includes characteristic two, and the level n may depend on the category.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4755, "coverage": "catalog_only", "read_detail": null, "pages": 26, "sha256": "49778ddd4cc611b5380fdc7227c695f1cb2de65983cf07783cae9be22bcb7071", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "209-01", "group": "209", "title": "An integral counterexample to Gersten's conjecture", "pdf": "preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf", "folder": "preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026", "abstract_original": "We construct a two-dimensional ramified regular local ring A of mixed characteristic $`(0,5)`$ for which $`K_5(A)\\to K_5(\\mathop{\\mathrm{Frac}}\\nolimits A)`$ has a nonzero kernel. This disproves Gersten's conjecture in its unrestricted integral form.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4771, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "c2fa194c832cce8cadb81dd45dfc1910bd385a1aa6456cdcac48315edbe04d61", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "209-02", "group": "209", "title": "An integral degree-three Gersten counterexample", "pdf": "preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf", "folder": "preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026", "abstract_original": "We construct a two-dimensional ramified regular local ring A in mixed characteristic $`(0,5)`$ for which the integral map $`K_3(A)\\to K_3(\\mathop{\\mathrm{Frac}}\\nolimits A)`$ has nonzero kernel. This gives a negative answer to the unrestricted integral Gersten conjecture.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4780, "coverage": "catalog_only", "read_detail": null, "pages": 10, "sha256": "c411abf2a5b4f0dd47ce13d1d22c79eca53abbcf1097c0b9e195ddf8b7856f7c", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "210-01", "group": "210", "title": "Foulkes' conjecture for the sixth symmetric power", "pdf": "preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf", "folder": "preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026", "abstract_original": "We prove the sixth-symmetric-power case of Foulkes' conjecture. For every integer b ≥ 6 and every finite-dimensional complex vector space V , there is a $`\\mathop{\\mathrm{GL}}\\nolimits (V)`$-equivariant injection $`\\mathop{\\mathrm{Sym}}\\nolimits ^6(\\mathop{\\mathrm{Sym}}\\nolimits ^b V)\\hookrightarrow\\mathop{\\mathrm{Sym}}\\nolimits ^b(\\mathop{\\mathrm{Sym}}\\nolimits ^6 V)`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4796, "coverage": "catalog_only", "read_detail": null, "pages": 36, "sha256": "6439c44d77b7de4bd1d9a3425a35e2f2ef2e21036609f77652167f95c8daa94d", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "210-02", "group": "210", "title": "Quadratic stabilization of the canonical Foulkes--Howe map", "pdf": "preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf", "folder": "preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026", "abstract_original": "For every finite-dimensional complex vector space V , we prove that the canonical Foulkes–Howe map $`\\mathop{\\mathrm{Sym}}\\nolimits ^b(\\mathop{\\mathrm{Sym}}\\nolimits ^a V)\\longrightarrow\\mathop{\\mathrm{Sym}}\\nolimits ^a(\\mathop{\\mathrm{Sym}}\\nolimits ^b V)`$ is surjective whenever a ≥ 2 and $`b\\ge a(a-1)`$. This gives a quadratic stabilization bound independent of $`\\dim V`$.", "archive": "math_research_01_of_08.zip", "exists": true, "source_line": 4805, "coverage": "catalog_only", "read_detail": null, "pages": 7, "sha256": "16b2feef6f939f6cf5bda458ab6392860a1a2a1a1dcb27c594960023625ec667", "bundled_pdf": null, "local_href": "../math_sources/math_research_01_of_08/preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" } ], "extra_folders": [] }