{ "archive": { "archive": "math_research_05_of_08.zip", "sha256": "e81788815f68b83e57d8b96846c2b0f90571ba3a2f3aeede15ea181428659d13", "bytes": 67505172, "crc_ok": true, "files": 1558, "physical_work_folders": 96, "preprint_pdfs": 103, "groups": [ "031", "211", "212", "213", "214", "215", "216", "217", "218", "219", "220", "285", "286", "287", "288", "289", "290", "291", "292", "293", "294", "295", "296", "297", "298", "299", "300", "301", "302", "303", "362", "363", "364", "365", "366", "367", "368", "369", "370", "371", "372", "373", "374", "375", "376", "377" ], "current_manuscripts": 96 }, "reading_policy": "Archive catalog parsed; PDFs opened structurally; only explicit read_detail entries represent actual reading.", "works": [ { "id": "031-01", "group": "031", "title": "Open Homomorphisms of Global Solvably Closed Galois Groups", "pdf": "preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf", "folder": "preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026", "abstract_original": "We prove Uchida's conjecture on open homomorphisms of Galois groups. Every continuous open homomorphism between Galois groups of solvably closed Galois extensions of number fields is induced by a unique equivariant field embedding in the opposite direction. No restriction on the kernel or additional compatibility hypothesis is required.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 746, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "36a58d5f408acc3d5430e1da1397aaaa7900321c3322a2001dcf7e6fc4de7fc0", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-01", "group": "211", "title": "Random Walks on Critical FK–Ising Maps and Liouville Brownian Motion", "pdf": "preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf", "folder": "preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026", "abstract_original": "We prove that stationary random walks on critical spherical FK–Ising planar maps converge to Liouville Brownian motion on the ordinary unit-area $`\\sqrt3`$-quantum sphere, using the geometric and electrical results of the spectral companion. The walk chooses uniformly among all incident half-edges, retaining loops and multiple edges. With the corner measure as the stationary law, the deterministic time acceleration is exactly the number of map edges. For any deterministic metric scale giving the metric-measure limit, convergence retains that same surface and any fixed finite number of conditionally independent walks with their time parameters.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4821, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "17d701d41c4cfec4dc7bbb2776b9879177befad75dd722de8241c611a2230abc", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Random-Walks-on-Critical-FK-Ising-Maps-and-Liouville-Brownian-Motion-October-5-2026/fk-ising-walk-limit.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-02", "group": "211", "title": "Spectral convergence for critical FK–Ising planar maps", "pdf": "preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf", "folder": "preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026", "abstract_original": "Using the conformal and metric-measure companion results and the stated Brownian/Liouville quantum gravity inputs, we prove spectral convergence for critical spherical FK–Ising maps to Liouville Brownian motion on the ordinary unit-area $`\\sqrt3`$-quantum sphere. The discrete walk has total attempt rate one, uses every map edge including loops and multiplicities, and has the corner measure as its stationary law. Accelerating time by the number of map edges gives joint convergence of the metric-measure space, all ordered eigenvalues with multiplicities and padding, and the heat trace locally uniformly at strictly positive times. The conductivity and clock constant are one in these conventions.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4830, "coverage": "catalog_only", "read_detail": null, "pages": 90, "sha256": "eeb5895c7058765f47abbbd62b52201464e8e6caad49ff88e49efec059ef48f4", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Spectral-convergence-for-critical-FK-Ising-planar-maps-October-5-2026/spectral-convergence-critical-fk-ising-planar-maps.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-03", "group": "211", "title": "A Linear Clock for Random Walk on Tree-Weighted Planar Maps", "pdf": "preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf", "folder": "preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026", "abstract_original": "We prove that stationary random walk on a planar map sampled with weight equal to its number of spanning trees converges to Liouville Brownian motion on the unit-area $`\\sqrt2`$-Liouville quantum sphere. The convergence retains the conditional path law jointly with the measured metric space. The walk chooses uniformly among all incident half-edges and starts from the stationary degree measure. For total attempt rate one and the continuum Dirichlet form with factor 1/2, the time acceleration is exactly the number of map edges. The result uses the companion contour and metric limits for this same ensemble.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4839, "coverage": "catalog_only", "read_detail": null, "pages": 59, "sha256": "0acb1c84bf79e9c86c03d6e1346b607ff7bcef8241321e49adf5ffb52f2aeec6", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-04", "group": "211", "title": "Canonical conformal limits of subcritical FK planar maps", "pdf": "preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf", "folder": "preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026", "abstract_original": "For every fixed $`0\\lt q\\lt 4`$, we prove joint convergence of spherical Fortuin–Kasteleyn planar maps in their flag-triangle uniformization to the corresponding unit-area Liouville quantum gravity sphere decorated by an independent conformal loop ensemble. The convergence includes the area measure, deterministically rescaled graph distances between all vertex pairs, and the full nested interface collection, with interfaces converging uniformly up to reparameterization.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4848, "coverage": "catalog_only", "read_detail": null, "pages": 123, "sha256": "e7dab39caf7781761af083b5845f2ab7c6b8906eb127e098ed1b3a5a7143c320", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Canonical-conformal-limits-of-subcritical-FK-planar-maps-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-05", "group": "211", "title": "The critical Liouville quantum sphere and geometric limits of FK maps at q=4", "pdf": "preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf", "folder": "preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026", "abstract_original": "We construct the field and area law of the unit-area critical Liouville quantum sphere as a limit of ordinary subcritical quantum spheres, and equip it with its critical intrinsic metric. We then prove that spherical Fortuin–Kasteleyn planar maps at q = 4, embedded by their equilateral flag uniformizations, converge jointly to this sphere decorated by an independent nested conformal loop ensemble CLE 4 . With deterministic distance normalization, the convergence includes the area measure, the full embedded distance function, and every macroscopic interface through all positive integer edge counts.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4857, "coverage": "catalog_only", "read_detail": null, "pages": 217, "sha256": "9b9236021eab20eb8a10c738b4089275f9b3b07e293e59f0e8c91410acae8857", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-critical-Liouville-quantum-sphere-and-geometric-limits-of-FK-maps-at-q-equals-4-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-06", "group": "211", "title": "Metric-measure limits of subcritical FK and spanning-tree planar maps", "pdf": "preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf", "folder": "preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026", "abstract_original": "We resolve the finite spherical cases of Gwynne and Miller's graph-metric conjecture for critical Fortuin–Kasteleyn maps at each fixed $`q\\in(0,4)`$ and for uniform spanning-tree-decorated maps. After deterministic rescaling of graph distances, these maps, equipped with the vertex probability measure proportional to degree, converge in Gromov–Hausdorff–Prokhorov law to their ordinary unit-area Liouville quantum gravity spheres. Distances use every primal edge, and convergence holds through all positive integer edge counts.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4866, "coverage": "catalog_only", "read_detail": null, "pages": 232, "sha256": "1dd659698d3a3fde21299449b3b293406538c97ccf711b334e74cb7dd138e9d0", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "211-07", "group": "211", "title": "Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four", "pdf": "preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf", "folder": "preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026", "abstract_original": "We prove the finite-volume continuum-random-tree prediction for critical Fortuin–Kasteleyn planar maps at every fixed q > 4. After rescaling graph distances by a constant times n −1/2 , an n -edge map with normalized degree measure converges to the Brownian continuum random tree in the Gromov–Hausdorff–Prokhorov topology. The convergence holds through all positive integer sizes.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4875, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "0d730ea9a40f1505b3f3bb2fdd401859cae09c2a69b1bea5d4b6d9aa86d5c0af", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Brownian-continuum-random-tree-limits-of-finite-Fortuin-Kasteleyn-maps-above-four-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "212-01", "group": "212", "title": "No bigeodesics in planar first-passage percolation", "pdf": "preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf", "folder": "preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026", "abstract_original": "We prove that planar first-passage percolation with independent identically distributed nonnegative nonatomic edge weights has almost surely no doubly infinite geodesic, provided the minimum of four independent weights has finite second moment. This resolves the planar no-bigeodesics conjecture under that moment assumption. The conclusion rules out all bigeodesics simultaneously, without any regularity assumption on the limit shape.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4891, "coverage": "catalog_only", "read_detail": null, "pages": 39, "sha256": "f97d87dc82bcee0cd11725e3261df8ddf51c34442c8305873c27107074d3b5ae", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "212-02", "group": "212", "title": "Strict convexity and differentiability of the planar exponential first-passage limit shape", "pdf": "preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf", "folder": "preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026", "abstract_original": "We prove that the limit shape of undirected nearest-neighbor first-passage percolation on ℤ 2 with independent exponential edge weights is strictly convex and has a C 1 boundary. This resolves the strict convexity and differentiability conjectures for the planar exponential model. More generally, we prove differentiability of the time-constant norm for every Gamma edge-weight law with positive shape and rate.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4900, "coverage": "catalog_only", "read_detail": null, "pages": 95, "sha256": "7cc30ddbfd4419f1a70086572910499befee5076ba85776b70edc45020dccb1c", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "213-01", "group": "213", "title": "Critical bond and site percolation on the cubic lattice", "pdf": "preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf", "folder": "preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026", "abstract_original": "We prove that nearest-neighbor Bernoulli bond and site percolation on ℤ 3 have no infinite cluster at their respective critical parameters. The proof combines a finite connection inequality for independent hyperedges with a finite-scale extension estimate and an adaptive exploration.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4916, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "9c32c0ba2d3d7e3dd0b37c912a8690725773753784c9bdb08220c70bcff90d2a", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "213-02", "group": "213", "title": "No percolation at criticality on quasi-transitive graphs", "pdf": "preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026/paper.pdf", "folder": "preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026", "abstract_original": "We prove that critical Bernoulli bond percolation has no infinite cluster on any infinite connected locally finite quasi-transitive graph with critical probability less than one. This resolves the bond form of the criticality conjecture of Benjamini and Schramm.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4925, "coverage": "catalog_only", "read_detail": null, "pages": 42, "sha256": "5929ccea200fd7433c5ac519c924316ccdd56fc0208ea0cc65d5a424bb2e425f", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/No-percolation-at-criticality-on-quasi-transitive-graphs-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "214-01", "group": "214", "title": "Nonuniqueness of percolation on nonamenable quasi-transitive graphs", "pdf": "preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026/paper.pdf", "folder": "preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026", "abstract_original": "We prove the bond-percolation nonuniqueness conjecture of Benjamini and Schramm: every infinite connected, locally finite, nonamenable quasi-transitive graph has a nonempty interval of parameters for which Bernoulli bond percolation almost surely has infinitely many infinite clusters. We also prove Hutchcroft's stronger operator-threshold conjecture, establishing $`p_c\\lt p_{2\\to2}\\le p_u`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4941, "coverage": "catalog_only", "read_detail": null, "pages": 53, "sha256": "46a78d044d2713e48cb3faa9b0b9d22da9480193e2202fe63d8e0daa7d8a3dbb", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nonuniqueness-of-percolation-on-nonamenable-quasi-transitive-graphs-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "215-01", "group": "215", "title": "The canonical massive continuum limit of the two-dimensional O(3) model", "pdf": "preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf", "folder": "preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026", "abstract_original": "We construct a canonical interacting massive continuum limit of the two-dimensional nearest-neighbor $`O(3)`$ model with unit-length spins, no external field, and no topological term. Normalized by susceptibility and second-moment correlation length, the limit exists as the bare coupling tends to infinity through all positive real values, without selecting subsequences. The limiting fields satisfy the Osterwalder–Schrader axioms and have a nonzero connected four-point correlation on separated time supports. Their reconstructed theory has a unique vacuum, a nonzero vacuum complement, and a positive Hamiltonian gap on that entire complement.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4957, "coverage": "catalog_only", "read_detail": null, "pages": 122, "sha256": "e75bfb353c2d3374503bbb899eb01dc21c94ed49fede6b3eb48f7ffce64527b2", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "215-02", "group": "215", "title": "An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field", "pdf": "preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf", "folder": "preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026", "abstract_original": "We consider the continuum spin field constructed from the nearest-neighbor two-dimensional $`O(3)`$ model by the fixed prescription of the companion paper. We prove that its vector two-point spectral measure has a positive atom corresponding to the lowest mass, separated by a positive gap from all remaining mass support.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4966, "coverage": "catalog_only", "read_detail": null, "pages": 26, "sha256": "302c6b61d389fbb901805a139403c61d60aebff745f32641172a55d66788384c", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "215-03", "group": "215", "title": "Exact mass asymptotics for the two-dimensional O(4) lattice model", "pdf": "preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026/exact-mass-o4.pdf", "folder": "preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026", "abstract_original": "For the nearest-neighbor $`O(4)`$ model on the square lattice at inverse temperature β , we prove the exact low-temperature asymptotic $`\\displaystyle m_{\\mathrm{lat}}(\\beta)\\sim 32\\exp(\\pi/4-1/2)\\sqrt\\beta\\,\\exp(-\\pi\\beta) \\qquad (\\beta\\to\\infty).`$ Here the mass is the gap of the full Osterwalder–Schrader transfer operator, including rotation-invariant local-observable sectors, in units of one original lattice time step.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4975, "coverage": "catalog_only", "read_detail": null, "pages": 109, "sha256": "4eb3ab28f756532217d79b66690587de12f732cf71286ede8011f5397994a14c", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026/exact-mass-o4.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Exact-mass-asymptotics-for-the-two-dimensional-O4-lattice-model-October-5-2026/exact-mass-o4.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "215-04", "group": "215", "title": "Sharp mass bounds for the two-dimensional O(4) model", "pdf": "preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf", "folder": "preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026", "abstract_original": "We prove sharp mass bounds for the two-dimensional nearest-neighbor $`O(4)`$ model. For all sufficiently large inverse couplings β , the full transfer gap, including rotation-invariant local-observable sectors, is bounded above and below by positive multiples of $`\\sqrt\\beta e^{-\\pi\\beta}`$. We also prove that the model has a unique periodic local limit and a positive full gap at every finite β > 0, resolving the all-temperature lattice mass-generation conjecture for this periodic state. Under the stated cutoff scaling, the mass bounds are uniform in independently fixed physical units. A continuum spectral interpretation requires separate convergence hypotheses for the transfer semigroup and the block observables.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4988, "coverage": "catalog_only", "read_detail": null, "pages": 102, "sha256": "e87f407df77777cadabcce10347533a68e7744be365ecd40c9602acc1129baac", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "215-05", "group": "215", "title": "Exponential decay in two-dimensional classical O(n) models", "pdf": "preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf", "folder": "preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026", "abstract_original": "We prove exponential decay of two-point correlations for the classical nearest-neighbor $`O(n)`$ model on the square lattice, for every n ≥ 3 and every finite positive inverse temperature. The estimate is uniform over finite free-boundary subgraphs and bounded nonnegative edge strengths. This resolves positively the all-temperature exponential spin-decay conjecture for these models.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 4997, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "9c94c692eda095e40eac070fba05a3e5340b023e9afb4ce873cefa4d5a361c66", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-01", "group": "216", "title": "The critical logarithmic correction for the planar XY model", "pdf": "preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf", "folder": "preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026", "abstract_original": "We prove the critical logarithmic correction for the nearest-neighbor cosine XY model on the square lattice. Let $`C_{b_c}(r)`$ be the two-point correlation at critical inverse temperature, obtained by taking the free-box thermodynamic limit while the two sites remain r lattice steps apart along a coordinate axis. Then $`\\displaystyle C_{b_c}(r)=B_{\\mathrm{XY}}r^{-1/4}(\\log r)^{1/8}(1+o(1)), \\qquad B_{\\mathrm{XY}}\\in(0,\\infty),`$ as $`r\\to\\infty`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5013, "coverage": "catalog_only", "read_detail": null, "pages": 84, "sha256": "5c357d1c416119fa157cddaa3e06854fd47bc1020cb7a797949ee42544272a8a", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-02", "group": "216", "title": "Critical Center Magnetization in the Planar XY Model", "pdf": "preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "folder": "preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026", "abstract_original": "Assuming the stated critical-height, local-renormalization, and spin-field inputs from the companion papers, we determine the center magnetization of the planar XY model in a square with aligned boundary spins at its mass-defined critical threshold. As $`n\\to\\infty`$, the magnetization is $`A_{\\mathrm{XY}}n^{-1/8}(\\log n)^{1/16}(1+o(1))`$, where $`A_{\\mathrm{XY}}`$ is a finite, strictly positive model-specific constant.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5026, "coverage": "catalog_only", "read_detail": null, "pages": 61, "sha256": "8347485745eaf5838417cebd36128198c7520b4e651091cb0f0ad8944ab87d1f", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-03", "group": "216", "title": "The Critical Spin Field of the Planar XY Model", "pdf": "preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf", "folder": "preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026", "abstract_original": "Using the companion critical Bessel-height and pin-limit theorems, we prove that at the mass-defined critical inverse temperature of the nearest-neighbor XY model on the square lattice, the spin field on a square with boundary angles fixed to zero converges along the full sequence to the full-variance imaginary exponential of a zero-Dirichlet Gaussian free field with stiffness $`2/\\pi`$. The normalization uses the exact center magnetization and the lattice Green-function factor. Convergence holds in law in $`H^{-3}_{\\mathrm{loc}}((-1,1)^2)`$; all mixed moments and joint laws of fields smeared against smooth compactly supported test functions in $`(-1,1)^2`$ converge as well.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5035, "coverage": "catalog_only", "read_detail": null, "pages": 43, "sha256": "486481fbcc54fe62c8d14e4f4a65869facc2a7f8a4c32647649468f91825ac47", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-04", "group": "216", "title": "Essential Singularity of the Correlation Length in the Planar XY Model", "pdf": "preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "folder": "preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026", "abstract_original": "We prove the Berezinskii–Kosterlitz–Thouless essential singularity for the correlation length of the nearest-neighbor cosine XY model on the square lattice. Let $`m(b)`$ be the mass obtained by taking first the free-box thermodynamic limit and then the separation limit along a coordinate axis. As the inverse temperature b approaches b c from the massive side, $`\\displaystyle \\sqrt{b_c-b}\\log\\frac{1}{m(b)} \\longrightarrow A_{\\mathrm{XY}},`$ where $`A_{\\mathrm{XY}}`$ is a finite, strictly positive model-specific constant.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5044, "coverage": "catalog_only", "read_detail": null, "pages": 54, "sha256": "5630748347a3657af3940a9429b440b420fcc31b6fdc96beedb348ae0b68f5a2", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-05", "group": "216", "title": "The critical correlation exponent of the planar XY model", "pdf": "preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf", "folder": "preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026", "abstract_original": "For the ordinary nearest-neighbor XY model on the square lattice, we prove the Berezinskii–Kosterlitz–Thouless prediction that the critical spin-correlation exponent is 1/4. More precisely, at the mass-defined critical inverse temperature, the infinite-volume correlation is $`n^{-1/4+o(1)}`$. The infinite-volume limit through free square boxes is taken before the separation limit.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5057, "coverage": "catalog_only", "read_detail": null, "pages": 50, "sha256": "e58587be77cd0256a9c426942dbc656bf3ae679cc4681a5e196bb333825eba17", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "216-06", "group": "216", "title": "BKT universality for height and planar spin fields", "pdf": "preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf", "folder": "preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026", "abstract_original": "We prove Gaussian scaling limits for the two-dimensional discrete Gaussian height model throughout its rough phase, including the physical roughening threshold, for every finite square-symmetric interaction set containing the nearest neighbors. After the natural lattice normalization, the critical effective temperature has the universal value $`8\\pi`$. For the ordinary nearest-neighbor Villain and XY models at sufficiently low fixed temperatures, we also prove that their Green-function-normalized spin fields converge to the imaginary exponential of a Dirichlet Gaussian free field.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5066, "coverage": "catalog_only", "read_detail": null, "pages": 169, "sha256": "5e6a8df09e021c4a114360d4bda50622ccac64d51150045a3df299565b133152", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "217-01", "group": "217", "title": "The low-temperature Sherrington–Kirkpatrick free-energy limiting law", "pdf": "preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf", "folder": "preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026", "abstract_original": "For every fixed inverse temperature β > 1, we prove that the zero-field Gaussian Ising Sherrington–Kirkpatrick free energy, centered by its expectation and divided by its standard deviation, converges in distribution to a nondegenerate law as the system size tends to infinity through all integers. We also prove that its variance divided by n 1/3 converges to a finite positive constant.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5082, "coverage": "catalog_only", "read_detail": null, "pages": 126, "sha256": "4acb0e456988f38e983358e468eeda74dc556c7b9bbd714f99da25ca94d07e7c", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "217-02", "group": "217", "title": "The low-temperature Sherrington–Kirkpatrick fluctuation scale", "pdf": "preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf", "folder": "preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026", "abstract_original": "For the zero-field Gaussian Sherrington–Kirkpatrick model at every fixed inverse temperature β > 1, we prove that the standard deviation of the log partition function is $`n^{1/6+o(1)}`$. The same exponent describes its typical centered absolute fluctuations, establishing the predicted one-sixth exponent in this regime.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5091, "coverage": "catalog_only", "read_detail": null, "pages": 80, "sha256": "e0e2e5e34169e701ff4bbd43736a3b9ea0dcee3c40606d78a36e844c86a3a4d9", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-01", "group": "218", "title": "Quenched SLE₃ limits for general weak random-bond Ising models", "pdf": "preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026/general-weak-random-bond-ising.pdf", "folder": "preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026", "abstract_original": "For the planar Ising model with bonds $`J_e=1+\\varepsilon\\xi_e`$, where the ξ e have any fixed bounded, nondegenerate, mean-zero iid law, we prove quenched chordal SLE 3 convergence for sufficiently small ε > 0. The temperature is the spontaneous-magnetization threshold. Convergence holds in probability over environments for the full oriented curve law in deterministic Jordan-domain approximations.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5107, "coverage": "catalog_only", "read_detail": null, "pages": 37, "sha256": "c693f39898f6f7d74f74cbe919a87b34267ca03e60e62e9efde72df23130756a", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026/general-weak-random-bond-ising.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Quenched-SLE3-limits-for-general-weak-random-bond-Ising-models-October-5-2026/general-weak-random-bond-ising.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-02", "group": "218", "title": "Quenched SLE₃ Universality for the Weak Random-Bond Ising Model", "pdf": "preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026/quenched-sle3-weak-random-bond-ising.pdf", "folder": "preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026", "abstract_original": "We prove quenched chordal SLE 3 convergence for the planar Ising model with sufficiently weak independent symmetric two-valued ferromagnetic bonds. The temperature is the critical point defined by spontaneous magnetization. Convergence holds in probability over environments for the full oriented curve law in deterministic Jordan-domain approximations.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5116, "coverage": "catalog_only", "read_detail": null, "pages": 57, "sha256": "dbf1578546653fc59b7ad8779a385741f0367c68f4147dc25e8ed251440fcb53", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026/quenched-sle3-weak-random-bond-ising.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Quenched-SLE3-Universality-for-the-Weak-Random-Bond-Ising-Model-October-5-2026/quenched-sle3-weak-random-bond-ising.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-03", "group": "218", "title": "Logarithmic Relative Fluctuations in the Weakly Disordered Planar Ising Model", "pdf": "preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf", "folder": "preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026", "abstract_original": "Assuming the stated deterministic critical-reference estimates, we prove that the relative second moment of the quenched critical spin correlation in the square-lattice Ising model with independent fair bonds $`1\\pm\\varepsilon`$ grows as $`(\\log r)^{1/4+o(1)}`$ for each sufficiently small fixed ε > 0. The correlation is evaluated at the physical critical temperature, with the thermodynamic limit taken before the disorder moments and the large-distance limit.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5125, "coverage": "catalog_only", "read_detail": null, "pages": 63, "sha256": "ec0e1bb240b41be6995f42f95c98f1d3252a95a5650352f12dd4111f9f90e8a3", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-04", "group": "218", "title": "Conformal universality of bulk Ising correlations under weak interactions", "pdf": "preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf", "folder": "preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026", "abstract_original": "We prove conformal universality of mixed bulk spin and energy correlations for the square-lattice Ising model with sufficiently small, square-symmetric, finite-range even multispin perturbations of either sign. One critical-temperature branch and two field normalizations apply in every bounded simply connected C 2 Jordan domain with free, plus, or minus boundary conditions, and in the periodic thermodynamic plane state. Energies are centered in their actual states.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5134, "coverage": "catalog_only", "read_detail": null, "pages": 53, "sha256": "8a815e7845436e07e663f9bc98ebc45fc642932a83bc9a0d35953ba32e5616c5", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-05", "group": "218", "title": "SLE3 universality for weak finite-range Ising interactions", "pdf": "preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf", "folder": "preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026", "abstract_original": "We prove that every sufficiently small, square-symmetric finite-range perturbation of the planar Ising contour energy has a domain-independent inverse temperature at which its spin interface converges to chordal SLE 3 . The result allows interactions of either sign, arbitrary admissible exterior contours, and uniformly approximated Jordan domains. Convergence holds for the full oriented curve law in uniform distance modulo increasing reparametrization.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5143, "coverage": "catalog_only", "read_detail": null, "pages": 76, "sha256": "44a7837e35328259a54a4c68311ad7f015175eed48681a8b1786d9cc00bc092c", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "218-06", "group": "218", "title": "Buffered comparison and stopping-band resolution in critical Ising", "pdf": "preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf", "folder": "preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026", "abstract_original": "We prove pointwise comparison and finite stopping-band approximation theorems for the critical nearest-neighbor Ising model on the square lattice. Arbitrary common pinned spins are allowed in the comparison: the likelihood ratio is controlled by a zero-field FK connection probability on the graph with those vertices deleted. For an interface exploration across a band of fixed positive width, finitely many regular signed barriers approximate every good conditional target law in total variation, uniformly over bounded observables and sufficiently fine meshes.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5152, "coverage": "catalog_only", "read_detail": null, "pages": 43, "sha256": "d5167e3fe5fb85f402954437c9474fb3ccfa518f8a5e8be92d8d572475410947", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Buffered-comparison-and-stopping-band-resolution-in-critical-Ising-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "219-01", "group": "219", "title": "Fixed-energy universality for weak Anderson disorder on random regular graphs", "pdf": "preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf", "folder": "preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026", "abstract_original": "For every fixed degree d ≥ 3, we prove fixed-energy GOE universality for the adjacency matrix of a uniformly random simple labelled d -regular graph with independent uniform diagonal disorder. The disorder strength is positive, sufficiently small, and fixed as the graph grows. At each fixed energy in a compact subinterval of the clean spectral band, the full microscopic eigenvalue point process converges to the GOE bulk process after rescaling by the positive density of states of the corresponding infinite-tree operator. The permitted disorder strength depends on the degree and the distance from the clean spectral edges.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5168, "coverage": "catalog_only", "read_detail": null, "pages": 60, "sha256": "b90d91abec2e8614ab12bfea2dc37152441e2651ec0482c70fc26665064e58b8", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "219-02", "group": "219", "title": "GOE bulk universality for fixed-degree random regular graphs", "pdf": "preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf", "folder": "preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026", "abstract_original": "We prove the fixed-degree bulk-universality conjecture for random regular graphs. For every fixed integer d ≥ 3 and every fixed energy in the open Kesten–McKay bulk, the unfolded eigenvalue point process of the adjacency matrix of a uniform simple labelled d -regular graph converges to the GOE bulk process. The convergence holds along all admissible graph sizes, without additional conditioning.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5177, "coverage": "catalog_only", "read_detail": null, "pages": 44, "sha256": "d8e092ab0484f8b9f8858176e39ab4c0cba5760450bf0a52890c6561ed2a7ced", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "220-01", "group": "220", "title": "A directional zero–one law for finite-range-dependent random environments", "pdf": "preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf", "folder": "preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026", "abstract_original": "We prove a directional zero–one law for uniformly elliptic nearest-neighbor random walks in stationary, ergodic, finite-range-dependent environments on ℤ d , d ≥ 3. For every fixed nonzero real direction, the probability of escape in that direction, averaged over the environment, is either zero or one. Finite-range dependence is imposed on the full transition rows: collections of rows at distance greater than a fixed range are independent, including collections indexed by infinite deterministic sets.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5193, "coverage": "catalog_only", "read_detail": null, "pages": 35, "sha256": "010edc479fd820382bf7dd600793ff5ab361216ce1ac06bb007f5505787cf958", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "220-02", "group": "220", "title": "A directional zero–one law under strict ellipticity", "pdf": "preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf", "folder": "preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026", "abstract_original": "We prove the directional zero–one conjecture for nearest-neighbor random walks in independent and identically distributed strictly elliptic environments on ℤ d , d ≥ 3: the probability of escape in each fixed nonzero real direction is zero or one. Only strict positivity of the transition probabilities is required; no uniform lower bound or moment assumption is imposed.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 5202, "coverage": "catalog_only", "read_detail": null, "pages": 34, "sha256": "245e917113b3545b311c4c9eab739227d530f527081c1b0be4a92ea904559683", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-directional-zero-one-law-under-strict-ellipticity-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "285-01", "group": "285", "title": "A torsion-free counterexample to reduced Baum–Connes injectivity", "pdf": "preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf", "folder": "preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026", "abstract_original": "We disprove rational injectivity of the coefficient-free reduced Baum–Connes assembly map for torsion-free groups. Specifically, we construct a finitely generated torsion-free discrete group whose degree-zero assembly map has a kernel class of infinite order.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7107, "coverage": "catalog_only", "read_detail": null, "pages": 85, "sha256": "df8d9301aa6d0306d7ac652e989c37a3c46b4c2285944694b746449157fc6714", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "285-02", "group": "285", "title": "A torsion-free counterexample to the Kadison–Kaplansky projection conjecture", "pdf": "preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf", "folder": "preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026", "abstract_original": "We construct a finitely generated torsion-free discrete group whose reduced group C ∗ -algebra contains a projection other than zero and the identity. This disproves the Kadison–Kaplansky projection conjecture.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7116, "coverage": "catalog_only", "read_detail": null, "pages": 76, "sha256": "df6227b61598580506210a8236216e043d1acd4ba062a9901b3063559ff62a5a", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Counterexample-to-the-Kadison-Kaplansky-Projection-Conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "285-03", "group": "285", "title": "An irrational-trace counterexample to reduced Baum–Connes", "pdf": "preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf", "folder": "preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026", "abstract_original": "We construct a finitely generated discrete group whose reduced group C ∗ -algebra contains a projection of irrational canonical trace. Its K 0 -class lies outside the image of the coefficient-free reduced Baum–Connes assembly map. This disproves the coefficient-free reduced Baum–Connes conjecture for countable discrete groups.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7125, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "4a9f78651b522ce79e99191bec9fe71a2c1ff505c9d3f991e8f401b0283e740e", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-Irrational-Trace-Counterexample-to-Reduced-Baum-Connes-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "286-01", "group": "286", "title": "Arithmeticity of twisted finite correspondences for lattices over local fields", "pdf": "preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf", "folder": "preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026", "abstract_original": "We prove arithmetic exhaustion for bifinite correspondences between arbitrarily scalar-twisted group factors of ICC groups commensurable with property-$`(T)`$ lattices over characteristic-zero local fields and twisted group factors of arbitrary countable ICC groups. Every such correspondence is a closed summand of a finite direct sum of models obtained from actual finite-index subgroup isomorphisms and finite-dimensional projective representations of the matched cocycle ratio. The proof includes reducible products, mixed real and finite places, and quaternionic and Cayley rank-one factors.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7141, "coverage": "catalog_only", "read_detail": null, "pages": 165, "sha256": "b1d070a5c4cd8496b98ff14e628572e2f0aa1b190f84ea3638398293e2e5ad01", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "286-02", "group": "286", "title": "The arithmetic category and stable recovery of lattice factors", "pdf": "preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf", "folder": "preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026", "abstract_original": "We prove stable canonical recovery for scalar-twisted group factors of ICC groups commensurable with property-$`(T)`$ lattices over characteristic-zero local fields. Every specified stable isomorphism to a scalar-twisted factor of any countably infinite ICC group recovers the group, the cocycle up to a normalized cochain, and equal amplification scales, with an implementing partial isometry in the given matrix corners. We compute the arithmetic correspondence subcategory for arbitrary countable ICC groups, including all bounded maps, summands, conjugates, and Connes fusion, and combine it with the companion's arithmetic exhaustion theorem. Multiplication also recovers arbitrary finite-index factor neighbors, with the exact projective condition on the matched cocycle ratio.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7150, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "b5a2107e608fdff7b8ccbab94cb652f474e156c9fb933a2b385d9edba8403ade", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "287-01", "group": "287", "title": "An isomorphism of the free group factors", "pdf": "preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf", "folder": "preprints/An-isomorphism-of-the-free-group-factors-September-23-2026", "abstract_original": "We solve the free group factor isomorphism problem affirmatively by proving that $`L(\\mathbb F_2)`$ and $`L(\\mathbb F_3)`$ are isomorphic as tracial von Neumann algebras. The classical free group factor alternative then implies that all interpolated free group factors, including $`L(\\mathbb F_\\infty)`$, are isomorphic and have fundamental group $`\\mathbb R_{\\gt 0}`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7166, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "e2000710ef969c50802cf398c64928bdfe92ea4925ce8bd9fb7a5b6bc4a232e1", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "288-01", "group": "288", "title": "Kadison's similarity theorem through uniform derivation estimates", "pdf": "preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf", "folder": "preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026", "abstract_original": "We prove that every bounded complex-linear unital algebra homomorphism from a unital complex C ∗ -algebra into the bounded operators on an arbitrary Hilbert space is similar to a $`*`$-homomorphism. This resolves Kadison's similarity conjecture positively. We also obtain one universal hyperreflexivity constant for all unital von Neumann algebras on arbitrary complex Hilbert spaces.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7182, "coverage": "catalog_only", "read_detail": null, "pages": 31, "sha256": "6c1ce1a87b0498395bf39facdf1eff7f474c294497798cc7cc51ba7ef0b491da", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "289-01", "group": "289", "title": "Universal strong Kadison–Kastler stability", "pdf": "preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf", "folder": "preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026", "abstract_original": "We prove that sufficiently close unital von Neumann algebras are conjugate by a unitary arbitrarily close to the identity. The tolerance depends only on the prescribed distance of that unitary from the identity, uniformly over all algebras, representations, and Hilbert spaces. This resolves the strong Kadison–Kastler conjecture.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7198, "coverage": "catalog_only", "read_detail": null, "pages": 70, "sha256": "3e801d4ed2d8c928e93581e9c4e53fd5d6c4a5ba0b1165ec61d83ae4b7f79691", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "289-02", "group": "289", "title": "Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings", "pdf": "preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026/near-inclusions.pdf", "folder": "preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026", "abstract_original": "We give a negative answer to the unrestricted small-spatial-embedding problem for one-sided near inclusions of von Neumann algebras. On separable complex Hilbert spaces, we construct pairs of unital von Neumann algebras with common identity whose one-sided gaps tend to zero. Spatial embeddings of the source into the target exist, but every implementing unitary stays a fixed positive distance from the identity. The obstruction therefore concerns small implementing unitaries, rather than the existence of spatial embeddings.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7207, "coverage": "catalog_only", "read_detail": null, "pages": 10, "sha256": "0e3e4d1bbe2ef13bd40ab9972a1361c3a8da9bd65eaf4f485db18618141bc4a9", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026/near-inclusions.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings-October-5-2026/near-inclusions.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "289-03", "group": "289", "title": "Close Separable C*-Algebras Without Spatial Conjugacy", "pdf": "preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf", "folder": "preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026", "abstract_original": "We disprove the separable C ∗ -algebraic spatial form of the Kadison–Kastler conjecture. For every ε > 0, we construct unital, norm-separable C ∗ -algebras on a common separable complex Hilbert space, with the same identity and Kadison–Kastler distance less than ε , that are not conjugate by any unitary. The two algebras have the same von Neumann closure.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7216, "coverage": "catalog_only", "read_detail": null, "pages": 9, "sha256": "1ea2edc84a981a7ec7287034d2af336e64e6fbff569a85d53517932294d8b903", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "290-01", "group": "290", "title": "Expected amenable subalgebras preserving core commutants", "pdf": "preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf", "folder": "preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026", "abstract_original": "We prove that every inclusion $`N\\subset M`$ of von Neumann algebras with separable preduals and a faithful normal conditional expectation contains an expected amenable subalgebra $`P\\subset N`$ such that $`P'\\cap c(M)=N'\\cap c(M)`$, where $`c(M)`$ denotes the continuous core of M . This resolves the relative bicentralizer conjecture in this setting.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7232, "coverage": "catalog_only", "read_detail": null, "pages": 19, "sha256": "af9a34e4fa4d0b23d115634d27d413f1013261dbe02b82802c3127c3b0efdb82", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "290-02", "group": "290", "title": "Bounded recovery for modular spectral averages", "pdf": "preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf", "folder": "preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026", "abstract_original": "We prove a bounded spectral recovery theorem for a von Neumann algebra with a faithful normal state whose centralizer consists only of scalars. A positive averaged squared norm for an arbitrary bounded Hilbert-space operator on shrinking modular spectral bands can be recovered on uniformly bounded algebra elements with shrinking spectral support. We apply this theorem to spectral intertwining rigidity and obtain an alternative proof of bicentralizer triviality for type III 1 factors with separable predual.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7241, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "7a0b0017ec76bdb23651398ca264127b0a6ad8159dd9f1e123e95f412eb33348", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026/Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "291-01", "group": "291", "title": "Equivariant Jiang–Su Stability for Amenable Actions in the Unital Stably Finite Case", "pdf": "preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf", "folder": "preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026", "abstract_original": "Every action of a countable discrete amenable group on a simple, separable, unital, infinite-dimensional, nuclear, stably finite complex C ∗ -algebra that is already Jiang–Su stable absorbs the trivial action on the Jiang–Su algebra up to cocycle conjugacy. No restriction is imposed on the action on the tracial-state simplex. This proves the unital, stably finite case of Szabó's Conjecture A on automatic equivariant Jiang–Su stability.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7257, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "99c6295ef166983a4d8f5213c49a0fc83a761d6e11996fd327bda41eed7971c4", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Equivariant-Jiang-Su-Stability-for-Amenable-Actions-in-the-Unital-Stably-Finite-Case-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "291-02", "group": "291", "title": "Cuntz comparison and Jiang–Su absorption", "pdf": "preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf", "folder": "preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026", "abstract_original": "We prove that strict comparison in the extended-functional sense implies Jiang–Su absorption for separable simple nuclear non-elementary C ∗ -algebras. This resolves the corresponding implication of the Toms–Winter regularity problem, including nonunital algebras and allowing unbounded traces. More generally, every separable nuclear C ∗ -algebra whose Cuntz semigroup is almost unperforated and fully almost divisible absorbs the Jiang–Su algebra.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7266, "coverage": "catalog_only", "read_detail": null, "pages": 65, "sha256": "5cbeda4528e0e671dcdb5cc55de6e32acb6bcd7e9bf219b905e2b3c206542e15", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "291-03", "group": "291", "title": "Nuclear dimension and Jiang–Su stability without elementary subquotients", "pdf": "preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026/paper.pdf", "folder": "preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026", "abstract_original": "For separable nuclear C ∗ -algebras with no nonzero elementary ideal subquotients, finite nuclear dimension is equivalent to Jiang–Su stability. More generally, $`\\dim_{\\mathrm{nuc}}(A_0\\otimes\\mathcal Z)\\le1`$ for every separable nuclear A 0 . This proves Robert and Tikuisis's Conjecture (C1) and the nuclear-dimension equivalence in the nonsimple Toms–Winter regularity question.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7275, "coverage": "catalog_only", "read_detail": null, "pages": 41, "sha256": "0a4fd7d8c4ac282e6be24e35ec777e3c853a5c47c62940a1cb6bac3f460e9715", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nuclear-dimension-and-Jiang-Su-stability-without-elementary-subquotients-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "291-04", "group": "291", "title": "Tracial projection methods and uniform property Gamma", "pdf": "preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf", "folder": "preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026", "abstract_original": "For a simple, separable, unital, infinite-dimensional, nuclear, stably finite C ∗ -algebra with traces, real rank zero of the uniform tracial ultrapower of its uniform tracial completion implies uniform property Γ. This answers Problem XXI of Schafhauser, Tikuisis and White affirmatively. Independently, strict comparison implies Jiang–Su absorption for simple, separable, unital, infinite-dimensional nuclear algebras, resolving the unital Toms–Winter conjecture. Under comparison tested on traces of finite target rank, we also obtain uniform property Γ and absorption for simple, separable, nuclear, stably projectionless algebras whose densely finite traces are all bounded and have a nonempty compact normalized base.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7284, "coverage": "catalog_only", "read_detail": null, "pages": 58, "sha256": "11c90e4d0861aa3f2aa91b50ba569111f1c35537bc19cac12b8c15e7fb6a565e", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Tracial-projection-methods-and-uniform-property-Gamma-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "292-01", "group": "292", "title": "An explicit obstruction to nuclear norm-ultrapower embeddings", "pdf": "preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf", "folder": "preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026", "abstract_original": "We give a negative answer to Kirchberg's norm-ultrapower embedding problem. We construct an explicit separable unital full group C ∗ -algebra that admits no unital embedding into B ω , for any nonzero unital nuclear C ∗ -algebra B and any free ultrafilter ω on ℕ. In particular, it does not embed unitally into $`\\mathcal O_2^\\omega`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7300, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "4d38fbd185d56ad449e377de26b9ff2155485bda94fa89fc127304fe57117ad5", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "293-01", "group": "293", "title": "Invariant-projection counterexamples for every irrational rotation", "pdf": "preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf", "folder": "preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026", "abstract_original": "For every irrational angle, we construct a continuous nonnegative circle weight with exactly one zero and logarithmic integral $`-\\infty`$ whose weighted rotation has no nontrivial invariant projection in the associated hyperfinite type II 1 factor. This answers negatively the question of Zhu, Fang, and Shi, with the angle prescribed in advance. The resulting operator is nonzero and norm-quasinilpotent.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7316, "coverage": "catalog_only", "read_detail": null, "pages": 47, "sha256": "951244ce4ac9e346a2e4d302e600d6fc58939deabe495638c2bb9070d037bca0", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "293-02", "group": "293", "title": "Backward intertwiners and a transitive commutant", "pdf": "preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf", "folder": "preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026", "abstract_original": "We give a negative answer to the hyperinvariant-subspace problem by constructing, on every infinite-dimensional separable complex Hilbert space, a nonzero bounded norm-quasinilpotent operator with no nonzero proper closed hyperinvariant subspace. Its commutant is a proper strongly closed unital transitive complex operator algebra.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7325, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "793876a758c32d9ef3081ba193f22f86127a8b524ec17c92a091d7601a7928ef", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "294-01", "group": "294", "title": "A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness", "pdf": "preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf", "folder": "preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026", "abstract_original": "We refute Kaplansky's quasitrace conjecture by constructing a separable unital complex C ∗ -algebra that admits normalized 2-quasitraces but has no tracial state. As a consequence, we show that the minimal tensor product of two unital simple stably finite complex C ∗ -algebras can be properly infinite, even when one factor is the reduced free-group algebra $`C_r^*(\\mathbb F_2)`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7341, "coverage": "catalog_only", "read_detail": null, "pages": 16, "sha256": "c46465adfaef9b9fe3213d524a2c2cbee5015b686031c94192d1156a55dbde05", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "295-01", "group": "295", "title": "Vanishing of higher bounded Hochschild cohomology", "pdf": "preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf", "folder": "preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026", "abstract_original": "We prove that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with values in the algebra itself, has a bounded primitive. Together with the established degree-one inner-derivation theorem, this resolves the Kadison–Ringrose cohomology conjecture positively.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7357, "coverage": "catalog_only", "read_detail": null, "pages": 28, "sha256": "56ec913df9fbe4a2daf371eec1cb06ddc5b544cf9defc838aab540f33171f753", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "296-01", "group": "296", "title": "Relative generation and the generator problem for finite factors", "pdf": "preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf", "folder": "preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026", "abstract_original": "We prove that every type II 1 factor with separable predual is generated by one operator, equivalently by two self-adjoint operators. Combined with the established direct-integral reduction to this case, this gives an affirmative solution of the generator problem for von Neumann algebras with separable predual.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7373, "coverage": "catalog_only", "read_detail": null, "pages": 18, "sha256": "c5838d4e6aba1dc13c368ca778839478d1a7a6429ee068101b01c33dc97b6e89", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "297-01", "group": "297", "title": "A counterexample to Naimark's problem in ZFC", "pdf": "preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf", "folder": "preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026", "abstract_original": "We construct in ZFC a unital infinite-dimensional simple complex C ∗ -algebra with a faithful tracial state whose nonzero irreducible representations are all unitarily equivalent. This gives a negative answer to Naimark's problem without additional set-theoretic assumptions.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7389, "coverage": "catalog_only", "read_detail": null, "pages": 23, "sha256": "5f8f878435bb94400a8f7c0c556bfc48d4bfc00782aa68066b6d4dac2d1560a8", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "298-01", "group": "298", "title": "A finite-entropy separation of microstates and nonmicrostates free entropy", "pdf": "preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf", "folder": "preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026", "abstract_original": "We answer the finite-entropy equality question for microstates and nonmicrostates free entropy negatively. We construct a bounded self-adjoint tuple X in a von Neumann algebra with faithful normal tracial state such that $`-\\infty\\lt \\chi(X)\\leq\\chi^*(X)-\\tfrac12\\lt \\infty`$. Here χ is the original microstates entropy with an operator-norm cutoff and a limsup over matrix sizes. The counterexample uses a large but fixed number of variables.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7405, "coverage": "catalog_only", "read_detail": null, "pages": 15, "sha256": "ab386b728e4dff538471550751e4ed18fbd6daf4fec6bc7eb0fa89943eccc5ea", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-finite-entropy-separation-of-microstates-and-nonmicrostates-free-entropy-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "299-01", "group": "299", "title": "The Kirchberg–Rørdam character criterion", "pdf": "preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf", "folder": "preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026", "abstract_original": "We prove the Kirchberg–Rørdam character criterion: for every free ultrafilter on ℕ, a nonzero unital separable complex C ∗ -algebra absorbs the Jiang–Su algebra if and only if its norm central-sequence algebra has no characters. We also prove that the infinite minimal tensor power of every nonzero unital separable complex C ∗ -algebra without characters is $`\\mathcal Z`$-stable and contains a unital copy of $`\\mathcal Z`$.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7421, "coverage": "catalog_only", "read_detail": null, "pages": 21, "sha256": "a0e2d22982358ba17e10b17f35b88bd5b99667cbec11356d8f7400e2239fc5ea", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Kirchberg-Rordam-character-criterion-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "300-01", "group": "300", "title": "Approximation Paving over Arbitrary Maximal Abelian Subalgebras", "pdf": "preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "folder": "preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026", "abstract_original": "We prove the approximation-paving conjecture of Popa and Vaes for every maximal abelian subalgebra of a complex von Neumann algebra. For each $`0\\lt \\varepsilon\\lt 1`$, every self-adjoint operator is a strong limit of self-adjoint operators of norm at most three times its norm, each admitting a norm paving with error at most ε times the approximant's own norm. The number of projections is at most $`C\\varepsilon^{-6}`$ for a universal constant C . No separability or conditional-expectation hypothesis is required.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7437, "coverage": "catalog_only", "read_detail": null, "pages": 48, "sha256": "2207c8250f6c641648a4b0727652808477d85678d518a9c641e4ca3e81c7d809", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "300-02", "group": "300", "title": "Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras", "pdf": "preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "folder": "preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026", "abstract_original": "We prove the quadratic strong-operator paving conjecture of Popa and Vaes. For every $`0\\lt \\varepsilon \\lt 1`$, every self-adjoint element of a von Neumann algebra admits strong-operator paving over each maximal abelian subalgebra with at most $`5\\times10^8\\varepsilon ^{-2}`$ projections. The bound is uniform over representations and requires no separability or conditional-expectation assumption.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7446, "coverage": "catalog_only", "read_detail": null, "pages": 54, "sha256": "d0cda0544b3c1b1b0091af621b26c2e66e1ac55e9ecb36c9c824d0c149dc3f1f", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "301-01", "group": "301", "title": "The trace cone classifies Razak–Jacelon stabilizations", "pdf": "preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf", "folder": "preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026", "abstract_original": "We prove that the canonical topological cone of all extended lower-semicontinuous tracial weights determines a separable nuclear C ∗ -algebra after tensoring with the Razak–Jacelon algebra and the compact operators, answering Robert's trace-cone classification question positively. The isomorphism realizes the prescribed cone map, with arbitrary ideal structure and without a density assumption on the finite domains of the weights.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7462, "coverage": "catalog_only", "read_detail": null, "pages": 62, "sha256": "9cf38a67706f91fa455d81f1b60ed1c2bc9c591dacb0f36cbf17c17fb7e81bca", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "302-01", "group": "302", "title": "Filtered products and boundary-preserving compression in complex cobordism", "pdf": "preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf", "folder": "preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026", "abstract_original": "We prove that, in sufficiently large smash powers, an $`MU`$-null restriction to a finite pointed subcomplex becomes stably null on the entire union of products with a fixed positive proportion of restricted factors. This coherent vanishing theorem yields boundary-preserving compression of cube-valued maps on every compact metrizable input space. When the torus slot bundle embeds continuously into a trivial bundle of rank less than twice the source rank, the compression places a positive proportion of slots on their boundaries in arbitrarily large powers and fixes every original boundary slot exactly. An example at equality shows that the strict rank inequality cannot be removed.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7478, "coverage": "catalog_only", "read_detail": null, "pages": 25, "sha256": "c47745026b3a083ca4b0af6972dc8cb230415c0061915621435300c85290daf5", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Filtered-products-and-boundary-preserving-compression-in-complex-cobordism-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "302-02", "group": "302", "title": "Radius of comparison equals half the mean dimension", "pdf": "preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026/paper.pdf", "folder": "preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026", "abstract_original": "We prove the integer-action case of the Phillips–Toms conjecture: for every minimal homeomorphism of an infinite compact metrizable space, the radius of comparison of its crossed product equals one half of its mean dimension, including equality at infinity. For these systems, zero mean dimension and the small boundary property are equivalent to Jiang–Su stability and to finite nuclear dimension of the crossed product; in this case its nuclear dimension is at most one.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7487, "coverage": "catalog_only", "read_detail": null, "pages": 24, "sha256": "1097583ea21e73e4d81bc4364e046312b7d4b37bbed7ab94b50206d81fec6be6", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Radius-of-comparison-equals-half-the-mean-dimension-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "303-01", "group": "303", "title": "Weak pure infiniteness and O-infinity absorption", "pdf": "preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf", "folder": "preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026", "abstract_original": "We prove that every complex C ∗ -algebra in which each positive element is properly infinite is strongly purely infinite. This answers the ordinary-to-strong part of Kirchberg–Rørdam's comparison question. For exact algebras, we also prove that proper infiniteness of one fixed finite amplification of every positive element implies proper infiniteness of each positive element. Consequently, every separable nuclear algebra with this fixed-amplification property absorbs $`\\mathcal O_\\infty`$, without assumptions of unitality or simplicity.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 7503, "coverage": "catalog_only", "read_detail": null, "pages": 52, "sha256": "2de287a58acb717007da6bbb6085d3150fba826131877a26c4328565c9208aca", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "362-01", "group": "362", "title": "Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system", "pdf": "preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf", "folder": "preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026", "abstract_original": "We prove global existence and uniqueness for arbitrary smooth admissible initial data in the three-dimensional, one-species relativistic Vlasov–Maxwell system. The particle density is initially compactly supported, and the electromagnetic fields have finite energy and bounded derivatives of all orders. The solution remains smooth on every finite time interval. This resolves the large-data global classical regularity problem for this model, without size or symmetry restrictions on the data.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8779, "coverage": "catalog_only", "read_detail": null, "pages": 49, "sha256": "56691a44941097fa1a5131470d44c5bc23930faeda22836e177d2391252817d8", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "363-01", "group": "363", "title": "Nonuniqueness with local conservation for the hard-sphere Boltzmann equation", "pdf": "preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf", "folder": "preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026", "abstract_original": "We prove nonuniqueness for the three-dimensional periodic hard-sphere Boltzmann equation among global entropy solutions satisfying exact local conservation of mass, momentum, and kinetic energy. We construct one nonnegative initial density with bounded velocity support and finite mass, energy, and absolute entropy that gives rise to two distinct such solutions. Both are strongly continuous in L 1 , and their collision gain and loss terms are integrable with every polynomial velocity weight on every bounded time interval.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8795, "coverage": "catalog_only", "read_detail": null, "pages": 78, "sha256": "640850bc08703544037791cecd9d71f11d558b8333d7f990abbe3a604d805489", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "363-02", "group": "363", "title": "Nonuniqueness for the periodic hard-sphere Boltzmann equation", "pdf": "preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf", "folder": "preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026", "abstract_original": "We prove nonuniqueness for the periodic hard-sphere Boltzmann equation by constructing two distinct global renormalized solutions with the same nonnegative initial density on $`\\mathbb T^3\\times\\mathbb R^3`$. This density has bounded velocity support and finite mass, energy, and absolute entropy. Both solutions conserve local mass and total momentum and satisfy the global energy and entropy-dissipation inequalities. On a common initial interval, they are strongly continuous in L 1 , and their collision gains and losses are integrable.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8804, "coverage": "catalog_only", "read_detail": null, "pages": 65, "sha256": "9cf0253f6b105302000bb4fd09b7d579cab61b4f7e131b757a768d97b168fc4e", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "364-01", "group": "364", "title": "The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals", "pdf": "preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf", "folder": "preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026", "abstract_original": "We derive the nonlinear Boltzmann equation from a grand-canonical Newtonian gas with initial pair exclusion. We treat stable, finite-range radial potentials that are C 2 except for an allowed repulsive singularity at the origin, and C 1 initial probability densities with spatially summable Gaussian bounds on the density and its spatial gradient. All fixed-order rescaled factorial marginals converge in L 1 , uniformly throughout every finite interval on which the classical kinetic solution has a uniform Gaussian bound. The result allows attractive wells and dynamically formed clusters, without restrictions on the differential scattering cross-section.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8820, "coverage": "catalog_only", "read_detail": null, "pages": 69, "sha256": "dce9fe5976f17b8953a134a43868b1d12c988093963472be3ac5f31e9cac2066", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "364-02", "group": "364", "title": "Hard-sphere fluctuations on the regular Boltzmann lifespan", "pdf": "preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf", "folder": "preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026", "abstract_original": "We prove a finite-dimensional central limit theorem away from equilibrium for a deterministic grand-canonical hard-sphere gas in three dimensions. The initial probability density is smooth, with spatially summable Gaussian velocity bounds on the density and its spatial gradient. The limit holds on every finite interval on which the classical Boltzmann solution has uniform Gaussian velocity decay. The empirical measure is centered by its exact microscopic expectation. Its fluctuations converge to the Gaussian solution of the linear fluctuating Boltzmann equation.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8829, "coverage": "catalog_only", "read_detail": null, "pages": 54, "sha256": "e294d8e5097f8d0eb801331ebadbf09a4b03ad57dfa0e6bd60f96e3c5e370c02", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "365-01", "group": "365", "title": "Determination of a metric and a unitary connection from one boundary patch", "pdf": "preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf", "folder": "preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026", "abstract_original": "We prove that zero-frequency boundary measurements on any nonempty open boundary patch determine both a smooth Riemannian metric and a smooth unitary connection on the trivial Hermitian rank-two bundle over a compact connected smooth manifold of dimension at least three with smooth boundary. Both inputs and observations are restricted to the same patch. The metric and connection are determined up to a diffeomorphism and a unitary gauge that restrict to the identity on the measured patch.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8845, "coverage": "catalog_only", "read_detail": null, "pages": 50, "sha256": "8e1bdd3a9067234842406dba45efc9e8efae5be0cd72a6c09f6dceee8793badb", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "365-02", "group": "365", "title": "Smooth anisotropic uniqueness in the Calderón problem from one boundary patch", "pdf": "preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf", "folder": "preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026", "abstract_original": "We resolve the smooth anisotropic Calderón uniqueness problem with arbitrary same-patch measurements. A smooth Riemannian metric on a compact connected manifold of dimension at least three is determined, up to a diffeomorphism fixing the measured patch, by its zero-frequency Dirichlet-to-Neumann energy form with both input and observation on any nonempty open boundary patch.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8854, "coverage": "catalog_only", "read_detail": null, "pages": 43, "sha256": "1ec46ed64206d12d8fdca42ae7454db52571c0ba1eb458aaf234a6ddea061d39", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "365-03", "group": "365", "title": "Nonuniqueness for bounded measurable scalar conductivities in three dimensions", "pdf": "preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf", "folder": "preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026", "abstract_original": "We construct two distinct uniformly positive bounded measurable scalar conductivities on a ball in ℝ 3 with the same full Dirichlet-to-Neumann operator. Both conductivities equal one near the boundary. This gives nonuniqueness in the scalar Calderón problem at bounded measurable regularity.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8863, "coverage": "catalog_only", "read_detail": null, "pages": 33, "sha256": "35017573c88b681f3f029ffb443091aa6fd55d31f6bc7a1b3566e5a6675aa7bb", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "366-01", "group": "366", "title": "Interior regularity of planar Mumford–Shah minimizers", "pdf": "preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf", "folder": "preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026", "abstract_original": "We prove the interior regularity assertion of the planar Mumford–Shah conjecture for reduced absolute minimizers with bounded fidelity data. Every interior point of the closed discontinuity set has a neighborhood consisting of a $`C^{1,\\alpha}`$ arc, an arc ending at that point, or three such arcs meeting at 120 degrees. Only finitely many global connected components meet any relatively compact open set.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8879, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "5b03d80e25997de7403e22b6b0a0db1179ad2bc52a921929b6cfe3e47382db1b", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "367-01", "group": "367", "title": "The critical dimension for one-phase Bernoulli minimizers", "pdf": "preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf", "folder": "preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026", "abstract_original": "We prove that seven is the critical dimension for the one-phase Bernoulli problem: every nonzero one-homogeneous global minimizer in dimensions at most six is flat, while a nonflat one-homogeneous global minimizer exists in dimension seven. It follows that the interior free boundary of a local minimizer is smooth in dimensions at most six. In dimension n ≥ 7, its singular set has Hausdorff dimension at most $`n-7`$, and this bound is sharp. In dimension seven, the singular set is locally finite.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8895, "coverage": "catalog_only", "read_detail": null, "pages": 50, "sha256": "eb1a535a1d8a9dc4c87d9eba7f861d5eda65531b75ac473eb5a5cb3ab7d3f727", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026/The-critical-dimension-for-one-phase-Bernoulli-minimizers-September-24-2026.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "368-01", "group": "368", "title": "Strong diffeomorphic approximation in three dimensions for 1≤p≤2", "pdf": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026/main.pdf", "folder": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026", "abstract_original": "We resolve the three-dimensional Ball–Evans approximation problem for $`1\\le p\\le2`$. Every $`W^{1,p}`$ homeomorphism between arbitrary bounded domains in ℝ 3 is a strong $`W^{1,p}`$ limit of smooth diffeomorphisms onto the same target.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8911, "coverage": "catalog_only", "read_detail": null, "pages": 62, "sha256": "245e4bde0050d2096b8f8f0ee7576c1b61703ea81ebc4e60caf7ea027e50d3eb", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-1-le-p-le-2-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "368-02", "group": "368", "title": "Strong diffeomorphic approximation in three dimensions for p>2", "pdf": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026/main.pdf", "folder": "preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026", "abstract_original": "We resolve the three-dimensional Ball–Evans approximation problem for every finite p > 2. Every $`W^{1,p}`$ homeomorphism between arbitrary bounded domains in ℝ 3 can be approximated strongly in $`W^{1,p}`$ by smooth diffeomorphisms onto the same target.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8920, "coverage": "catalog_only", "read_detail": null, "pages": 130, "sha256": "824a96588feb42d52c6573fcbe7d30e4ffab0397d1830248e95fa9be94d90435", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "369-01", "group": "369", "title": "Strict hot spots and absence of interior critical points on smooth simply connected planar domains", "pdf": "preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf", "folder": "preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026", "abstract_original": "We prove the strict hot spots conjecture for smooth bounded simply connected planar domains. More precisely, every nonzero eigenfunction for the first positive Neumann eigenvalue has nonvanishing gradient in the interior, so all its global maxima and minima lie on the boundary. This holds even when the eigenvalue is multiple.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8936, "coverage": "catalog_only", "read_detail": null, "pages": 21, "sha256": "7a65d7bc83270c2b1eccc49a3921fd61bc281283b7d0c3a5059df0a2f8778413", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/main.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "370-01", "group": "370", "title": "The Subcritical Hénon–Lane–Emden Conjecture", "pdf": "preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf", "folder": "preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026", "abstract_original": "We prove the subcritical Hénon–Lane–Emden conjecture: for every dimension n ≥ 2, positive powers p , q , and real weights A , B , the system has no strictly positive entire solution when $`(n+A)/(p+1)+(n+B)/(q+1)\\gt n-2`$. Solutions need only be continuous at the origin and classical elsewhere, without a condition at infinity. For n ≥ 3 and $`A,B\\gt -2`$, combining this result with the radial existence theorem of Bidaut-Véron and Giacomini proves Phan's Conjecture C in full: a positive radial entire solution exists whenever the strict inequality fails.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8952, "coverage": "catalog_only", "read_detail": null, "pages": 20, "sha256": "bb18015a30854675bec22e3183996625dac9be5046f81838c0bf9fbfa88806dc", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "371-01", "group": "371", "title": "Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus", "pdf": "preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf", "folder": "preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026", "abstract_original": "We prove stable self-similar finite-time blowup for a supercritical defocusing nonlinear Schrödinger equation on the twelve-dimensional torus. For a sufficiently large odd power, the blowup initial data contain a nonempty open set in a high Sobolev space. As a consequence, Gaussian Fourier initial data of arbitrarily high Sobolev regularity can have positive probability of finite-time blowup.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8968, "coverage": "catalog_only", "read_detail": null, "pages": 56, "sha256": "09887025fcf6735415f357bf2bc3f92e2cb0f86c01ac5f59ac255406e58eee4b", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "372-01", "group": "372", "title": "Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem", "pdf": "preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf", "folder": "preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026", "abstract_original": "We prove that the full static displacement-to-traction map uniquely determines both real smooth Lamé moduli on every bounded connected smooth domain in ℝ 3 , provided μ > 0 and $`3\\lambda+2\\mu\\gt 0`$ on the closure. This resolves the smooth three-dimensional isotropic elastic Calderón uniqueness problem under these positivity assumptions.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 8984, "coverage": "catalog_only", "read_detail": null, "pages": 24, "sha256": "5cadfeb6eb45bea20b6ceb4879266d49938154c38dbf34a6531b47b4f3cfbff9", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "373-01", "group": "373", "title": "A counterexample to the Monge ansatz for the three-marginal Coulomb cost", "pdf": "preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026/paper.pdf", "folder": "preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026", "abstract_original": "We construct a smooth compactly supported probability density on ℝ 3 , with a smooth compactly supported square root, for which the three-marginal Coulomb transport minimum is not attained by any pair of measure-preserving Borel maps. Nevertheless, the Monge and Kantorovich infima agree: we construct preserving maps whose costs approach the Kantorovich minimum. For every d ≥ 2 and s > 0, we also construct a smooth identical marginal with the same nonattainment and equality-of-infima properties for the inverse-power interaction $`\\sum_{i\\lt j}|x_i-x_j|^{-s}`$ on ℝ d .", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9000, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "46caabb46552913329e6a1a6226ad2dc196bd231d117562d0495f19a5832ae70", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026/paper.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-Monge-ansatz-for-the-three-marginal-Coulomb-cost-September-25-2026/paper.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "374-01", "group": "374", "title": "Sharp One-Third Stability of Brenier Maps", "pdf": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf", "folder": "preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026", "abstract_original": "For the uniform probability measure ρ on a compact convex body in ℝ d , d ≥ 2, quadratic optimal transport maps are one-third Hölder continuous in $`L^2(\\rho)`$ with respect to the target's 2-Wasserstein distance. The constant is uniform over all targets supported in a fixed compact set, and the exponent is optimal. A three-atom family on a fixed cube disproves Letrouit's conjectured uniform square-root estimate.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9016, "coverage": "catalog_only", "read_detail": null, "pages": 18, "sha256": "e9821deea8e836aaae6ed84cfb489e3695e1d6ce36add7e14c54100d2209f184", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "375-01", "group": "375", "title": "A positive resolution of De Giorgi's conjecture in dimension eight", "pdf": "preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026/article.pdf", "folder": "preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026", "abstract_original": "We resolve De Giorgi's conjecture positively in dimension eight: every entire C 2 solution $`u:\\mathbb R^8\\to(-1,1)`$ of $`\\Delta u=u^3-u`$ with an everywhere positive directional derivative is a planar heteroclinic. We prove that every stable solution $`v:\\mathbb R^7\\to[-1,1]`$ of this equation is a constant well or a planar heteroclinic, without an energy-growth assumption.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9032, "coverage": "catalog_only", "read_detail": null, "pages": 97, "sha256": "6c92e90f31e12f32514f9366d101aa8edbc16007ca3147cfc193919abfff0e3f", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026/article.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/De-Giorgis-conjecture-in-dimension-eight-September-26-2026/article.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-01", "group": "376", "title": "Finite Instructions and Solenoidal Shear Flows", "pdf": "preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf", "folder": "preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026", "abstract_original": "We realize finite reciprocal affine instruction maps by smooth incompressible shear flows on a flat three-torus. Applied to a reversible one-head recorder with a finite transition table, this gives a complete machine-to-fluid construction: a fixed particle enters a fixed open strip exactly when a given machine halts, with zero initial velocity, zero pressure, and a solenoidal mean-zero force that is periodic after initialization. The construction acts on full closed rectangles and controls every intermediate trajectory. Separate heights resolve overlap between sources and targets, and an endpoint-size estimate controls all excursions independently of the reciprocal scaling factor.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9048, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "0cdc2abd5b1a3d152fe55f7793ccc3f49ec6e7a79d0f5b4893e10c1b2c061e8d", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-02", "group": "376", "title": "A Fixed Particle Test for Computation in a Forced Viscous Flow", "pdf": "preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf", "folder": "preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026", "abstract_original": "We construct smooth external forces for incompressible Navier–Stokes flow on a fixed flat three-torus at any fixed positive computable viscosity, from zero initial velocity, such that a fixed particle enters a fixed open set exactly when a prescribed Turing machine halts. Every mixed derivative of the force and velocity is bounded and square-integrable in time in spatial supremum norm. The construction uses the machine's ordinary instructions, records their history in a third coordinate, and compensates for finer spatial gates by longer time steps.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9057, "coverage": "catalog_only", "read_detail": null, "pages": 13, "sha256": "87defbd4577b4c8ef80cd148000ffd55e7b3d2ce296d27b04efb16aae92f8c0d", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-03", "group": "376", "title": "Universal Computation with Eventually Stationary Navier–Stokes Forcing", "pdf": "preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "folder": "preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026", "abstract_original": "At every fixed positive computable viscosity, we construct smooth mean-zero forces on the flat three-torus that become stationary after time one and make a fixed particle, initially in a fluid at rest, enter a fixed open set exactly when a prescribed Turing machine halts. The force has bounded derivatives of every order and a finite effective description. A reversible recording table is realized on whole planar rectangles by Hamiltonian motions, then driven by a mean-zero spatial clock. Separate choices give periodic forcing from time zero or a force whose derivatives are square-integrable in time.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9066, "coverage": "catalog_only", "read_detail": null, "pages": 14, "sha256": "0af659c5a6f8e7b07c66d3301055e8a80e616c938ffb6027272e42097374d0d5", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-04", "group": "376", "title": "Geometric Programs for Solenoidal Forcing", "pdf": "preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf", "folder": "preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026", "abstract_original": "We construct smooth solenoidal mean-zero forces, periodic from time zero, for which a fixed particle on a flat three-torus reaches a fixed open strip exactly when a given machine halts. The initial fluid velocity and the pressure are zero. We also realize positive diagonal maps on coding sheets by incompressible shears, with explicit normal compensation for changes of planar area, and reciprocal maps on whole boxes of positive thickness. Complete local inverses, initialization rules, and intermediate trajectory bounds connect these geometric constructions to finite computations.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9075, "coverage": "catalog_only", "read_detail": null, "pages": 29, "sha256": "1e54090582721ee2edcecf924b7c6176b8f6e3a5c037d861e6e6befb2cb6ba17", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-05", "group": "376", "title": "Prefix Instructions and Incompressible Flows", "pdf": "preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf", "folder": "preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026", "abstract_original": "Finite prefix instructions may change area and erase information. We give explicit history processors and smooth incompressible motions that retain that information and realize every instruction on its full domain. A first application assigns each machine and finite input a smooth mean-zero force on the flat unit three-torus, at any fixed positive computable viscosity. The solution starts from rest; a fixed particle enters a fixed open strip exactly when the machine halts. The force repeats with period one after an initial loading interval. We then prove alternative realizations using full boxes, normal compensation, invariant planes, and a spatial clock. The constructions specify their initialization, comparison class, derivative bounds, and continuous-time observation. Exact formulas and effective cutoffs provide finite descriptions of the fields and all their derivatives.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9084, "coverage": "catalog_only", "read_detail": null, "pages": 53, "sha256": "8cd581420ec9967ac33296ba4f91342cb275bd63db72d0db630139381d3aa59e", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-06", "group": "376", "title": "Computation under Rapidly Vanishing Navier–Stokes Forcing", "pdf": "preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "folder": "preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026", "abstract_original": "At any fixed positive computable viscosity, smooth forces can make a fixed fluid particle detect the halting of an arbitrary machine, starting from rest, while every mixed derivative of the force and velocity decreases faster than every inverse power of time. We give three complete memory constructions: compact moving curls, alternating fractional coordinates, and a periodic lattice on the flat three-torus. Each machine step takes one unit of physical time. The constructions retain earlier records at separated spatial scales and use an exact open detector with a shrinking signal.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9093, "coverage": "catalog_only", "read_detail": null, "pages": 19, "sha256": "931c07840228968ba5c7531964bb51266bdfc50915baa7f20b8ce15a57a6c551", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-07", "group": "376", "title": "Velocity-Field Detection of Computation in Forced Navier–Stokes Flows", "pdf": "preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf", "folder": "preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026", "abstract_original": "We construct smooth forces for three-dimensional incompressible Navier–Stokes flow, from rest at any fixed positive computable viscosity, whose velocity field detects whether a prescribed machine halts. On the unit flat torus, a pointwise test of the third velocity component uses successively shorter stirring intervals in a fixed spatial region. On $`\\mathbb R^2\\times\\mathbb T`$, an integral test uses an expanding array of translation regions and a force with globally bounded mixed derivatives. The vertical velocity solves an advection–diffusion equation: short bursts control its pointwise error in the first construction, and a moving cutoff controls the total escaped mass in the second.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9102, "coverage": "catalog_only", "read_detail": null, "pages": 18, "sha256": "a69fca6b458f542aefe5d21cd36fef355f37d7b22dc517474304888b847f00bc", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-08", "group": "376", "title": "Scalar Potentials and Slow Clocks for Forced Fluid Computation", "pdf": "preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf", "folder": "preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026", "abstract_original": "We construct smooth forces of fixed compact spatial support for three-dimensional incompressible Navier–Stokes flow from rest whose particle at the origin detects halting by entering a fixed half-space. Every mixed derivative of the force and velocity decays at rate $`O((1+t)^{-1-j})`$ for time order j . Three scalar potentials lift a coded rectangle, perform its instruction, and lower its image; an unbounded logarithmic clock supplies the decay. We also realize area-changing prefix instructions on an invariant torus plane, and construct a planar Hamiltonian processor admitting periodic forcing, stationary forcing after startup, and a velocity-field detector through a companion diffusion theorem.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9111, "coverage": "catalog_only", "read_detail": null, "pages": 22, "sha256": "82005335f0aac60fbd7f84ba2d4aee576671a54cc39b2662e263063e62ac45e1", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "376-09", "group": "376", "title": "Incompressible Box Transport and Finite Computation", "pdf": "preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf", "folder": "preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026", "abstract_original": "We realize finite positive diagonal affine maps of determinant one by effective smooth incompressible flows on neighborhoods of entire closed rational solid boxes. The source and target families are each disjoint, but may overlap each other. The construction uses localized curls, evacuation to storage and obstacle detours. A balanced three-stack recorder then assigns every machine and finite input a smooth Navier–Stokes force with one compact spatial support, periodic after a loading interval, at any fixed positive computable viscosity. The fluid starts at rest, and one fixed particle enters one fixed open cube exactly when the machine halts. Further constructions give fixed torus charts, periodicity from time zero, alternative history guards and bounded or slab observers. Onto slow clocks yield separate decaying forces. Each construction includes an all-time observation proof, effective derivative bounds and a stated pressure comparison class.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9120, "coverage": "catalog_only", "read_detail": null, "pages": 78, "sha256": "2505dc09d3f2c24b91b8a1bd4ae58876095f1d1407ead933464b79731ae5d312", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" }, { "id": "377-01", "group": "377", "title": "Uniform Interior $`C^{1,\\alpha}`$ Estimates for Infinity-Harmonic Functions", "pdf": "preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf", "folder": "preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026", "abstract_original": "We prove a uniform interior $`C^{1,\\alpha_d}`$ estimate for bounded infinity-harmonic functions in every dimension d ≥ 3. For some $`\\alpha_d\\in(0,1/3]`$ depending only on the dimension, the gradient's supremum norm and α d -Hölder seminorm on B 1/2 are bounded by a dimension-dependent constant times the oscillation on B 1 . The exponent is not explicit, and no endpoint or boundary regularity claim is made. In particular, infinity-harmonic functions are locally C 1 on every open subset of ℝ d , for d ≥ 3.", "archive": "math_research_05_of_08.zip", "exists": true, "source_line": 9136, "coverage": "catalog_only", "read_detail": null, "pages": 46, "sha256": "8c01e0c934ce3ef1149a40ad953d7b64702ab4297a64f150de2de905842c87d4", "bundled_pdf": null, "local_href": "../math_sources/math_research_05_of_08/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf", "online_url": "https://github.com/openai/math/blob/main/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf", "source_catalog": "sources/context/CONTENTS.md", "independent_verification": "not_identified_in_limited_search" } ], "extra_folders": [] }