qed.bot — what machines have actually proved https://qed.bot/ 2026-09-25T14:25:41Z Claims of AI contributions to mathematics, graded for autonomy and evidence. Existence And Smoothness Of The Navier–Stokes Equation — full (GPT-6 Astra) urn:qed:89ef9abfa51b 2026-09-09T00:00:00Z Formalised the Navier–Stokes and Euler results in Lean, checked with Comparator against the Formal Conjectures statements of alternatives (C) and (D).. Autonomy A1, evidence V2. Existence And Smoothness Of The Navier–Stokes Equation — full (OpenAI internal model) urn:qed:ed88695692e8 2026-09-08T00:00:00Z Finite-time blowup for the 3D incompressible Navier–Stokes equations with smooth forcing, on Euclidean space and on the torus: Fefferman's alternatives (C) and (D), a negative answer to the Millennium problem. Unforced Euler blowup is proved alongside.. Autonomy A2, evidence V2. Fermat's Last Theorem — full (Claude) urn:qed:2cba2d1d7d11 2026-09-04T00:00:00Z A complete Lean 4 proof of Fermat's Last Theorem on the standard axioms, deriving Mathlib's own statement, with the classical inputs proved in the strength the argument needs rather than assumed.. Autonomy A1, evidence V2. Erdős Problem 36 — candidate (GPT-5.5 Pro) urn:qed:3d73d278c8e8 2026-06-29T00:00:00Z Candidate partial result. Autonomy A3, evidence V0. Erdős 1070 — partial (Codex, GPT-5.5) urn:qed:3e886831430b 2026-06-29T00:00:00Z Partial result. Autonomy A1, evidence V1. Erdős 731 — candidate (GPT) urn:qed:ecb1a6355fe9 2026-06-27T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős 1033 — candidate (GPT-5.5 Pro) urn:qed:4930555daa29 2026-06-27T00:00:00Z Candidate partial result. Autonomy A3, evidence V0. Erdős Problem 730 — candidate (GPT-5.5 Pro) urn:qed:b06c5541a56d 2026-06-24T00:00:00Z Candidate full solution. Autonomy A3, evidence V0. Erdős Problem 1061 — candidate (GPT) urn:qed:33d27449433a 2026-06-24T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős Problem 593 — candidate (GPT) urn:qed:dfdf737cc1be 2026-06-23T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős 432 — candidate (GPT-5.5 Pro) urn:qed:00cad66cefa8 2026-06-23T00:00:00Z Candidate partial result. Autonomy A1, evidence V0. Erdős Problem 21 — partial (Aristotle, GPT-5.5 Pro) urn:qed:2c9f248e551c 2026-06-23T00:00:00Z Partial result (Lean). Autonomy A1, evidence V2. Erdős 176 — candidate (Codex, GPT-5.5 Pro) urn:qed:1aff9b408d56 2026-06-23T00:00:00Z Candidate partial result (Lean). Autonomy A3, evidence V0. Erdős 1177 — candidate (GPT) urn:qed:da1dfc1b4cfe 2026-06-23T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős Problem 1054 — partial (Claude Opus 4.8, GPT-5.5 Pro, Principia Math) urn:qed:0718d31147f0 2026-06-23T00:00:00Z Partial result (Lean). Autonomy A3, evidence V2. Erdős Problem 865 — full (GPT-5.5 Pro) urn:qed:4f3376d89ebe 2026-06-22T00:00:00Z Full solution. Autonomy A1, evidence V3. Erdős 768 — candidate (GPT) urn:qed:2cffd6455cdc 2026-06-22T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős 671 — candidate (Codex, GPT-5.5 Pro) urn:qed:ead34dae37b8 2026-06-22T00:00:00Z Candidate full solution (Lean). Autonomy A3, evidence V0. Erdős Problem 550 — candidate (GPT) urn:qed:4b0ad2e50880 2026-06-22T00:00:00Z Candidate full solution. Autonomy A3, evidence V0. Erdős Problem 536 — partial (Codex, GPT-5.5 Pro) urn:qed:45803743c5ee 2026-06-22T00:00:00Z Partial result (Lean). Autonomy A3, evidence V2. Erdős Problem 512 — full (Aristotle) urn:qed:677202a69ea4 2026-06-22T00:00:00Z McGehee, Pigno, and Smith (1981). Autonomy A1, evidence V3. Erdős Problem 400 — candidate (GPT) urn:qed:d0d65ca90dc9 2026-06-22T00:00:00Z Candidate partial result. Autonomy A1, evidence V0. Erdős Problem 948 — full (Aristotle, GPT-5.5 Pro) urn:qed:a2cae790a0c9 2026-06-21T00:00:00Z Full solution (Lean). Autonomy A2, evidence V2. Erdős Problem 464 — full (Aristotle) urn:qed:b7a30a74bcef 2026-06-21T00:00:00Z de Mathan (1980). Autonomy A1, evidence V3. Erdős Problem 346 — full (Codex, GPT) urn:qed:51a915ecd033 2026-06-21T00:00:00Z Full solution (Lean). Autonomy A1, evidence V3. Erdős 176 — partial (Codex, GPT-5.5 Pro) urn:qed:55859d8a9d9f 2026-06-21T00:00:00Z Partial result (Lean). Autonomy A3, evidence V2. Erdős Problem 1197 — full (Aristotle, Claude Opus 4.7, GPT-5.4 Pro) urn:qed:b6a97e12c2cf 2026-06-21T00:00:00Z Full solution (Lean). Autonomy A2, evidence V2. Erdős 716 — full (Aristotle) urn:qed:f80c2ed447b7 2026-06-20T00:00:00Z Ruzsa and Szemerédi (1978). Autonomy A1, evidence V1. Erdős Problem 353 — full (Aristotle) urn:qed:10d5f528cced 2026-06-20T00:00:00Z Kovač and Predojević (2024) + Koizumi (2025). Autonomy A1, evidence V3. Erdős Problem 1095 — partial (Aristotle) urn:qed:555194c7db58 2026-06-20T00:00:00Z Konyagin (1999). Autonomy A1, evidence V1. Erdős 81 — partial (Aristotle, GPT-5.5 Pro) urn:qed:494161c1848c 2026-06-19T00:00:00Z Partial result (Lean). Autonomy A1, evidence V2. Erdős 451 — partial (Aristotle, GPT-5.5 Pro) urn:qed:1363b4beee38 2026-06-19T00:00:00Z Partial result (Lean). Autonomy A1, evidence V2. Erdős Problem 441 — partial (AxiomProver) urn:qed:a8de9e7f1351 2026-06-19T00:00:00Z Chen and Dai (2007). Autonomy A1, evidence V1. Erdős Problem 403 — full (AxiomProver) urn:qed:83ad9b858e23 2026-06-19T00:00:00Z Unspecified. Autonomy A1, evidence V3. Erdős Problem 346 — partial (Codex, GPT-5.5 Pro) urn:qed:8c3caff2bf2e 2026-06-19T00:00:00Z Solution to variant problem (Lean). Autonomy A3, evidence V3. Erdős Problem 328 — full (AxiomProver) urn:qed:9717094565e7 2026-06-19T00:00:00Z Nešetřil and Rödl (1985). Autonomy A1, evidence V3. Erdős Problem 306 — candidate (Unspecified) urn:qed:f4944bb39039 2026-06-19T00:00:00Z Candidate full solution (Lean). Autonomy A1, evidence V0. Erdős Problem 209 — full (AxiomProver) urn:qed:32d65f2b9c5d 2026-06-19T00:00:00Z Escudero (2016). Autonomy A1, evidence V3. Erdős Problem 1139 — candidate (GPT-5.2 Pro, GPT-5.5 Pro) urn:qed:1daccb189823 2026-06-19T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős Problem 1134 — full (AxiomProver) urn:qed:00fa638da55b 2026-06-19T00:00:00Z Unspecified. Autonomy A1, evidence V1. Erdős Problem 306 — partial (Claude, Claude Code) urn:qed:5ec141d2eeff 2026-06-17T00:00:00Z Partial result (Lean). Autonomy A1, evidence V2. Erdős Problem 986 — full (Claude, OpenAI internal model) urn:qed:4cb62d1bc8be 2026-06-16T00:00:00Z Full solution. Autonomy A1, evidence V1. Erdős Problem 942 — partial (Aristotle, Claude Opus 4.8, Codex, GPT-5.5) urn:qed:7b49df676206 2026-06-14T00:00:00Z Partial result (Lean). Autonomy A1, evidence V2. Erdős Problem 326 — full (Aristotle, Codex, GPT-5.5) urn:qed:338e7180aa31 2026-06-14T00:00:00Z Full solution (Lean). Autonomy A1, evidence V2. Erdős 1208 — candidate (GPT-5.5 Pro) urn:qed:7a2ad60ed190 2026-06-14T00:00:00Z Candidate partial result. Autonomy A1, evidence V0. Erdős Problem 90: The unit distance problem — full (Aleph Prover) urn:qed:e84c27a326fd 2026-06-12T00:00:00Z OpenAI internal model (2026). Autonomy A1, evidence V1. Erdős Problem 986 — partial (Trellis) urn:qed:413f06cefa6d 2026-06-10T00:00:00Z Bradač (2026). Autonomy A1, evidence V1. Erdős Problem 539 — partial (Codex, GPT-5.5, ProofCouncil) urn:qed:3c8bb4580bc2 2026-06-10T00:00:00Z Partial result (Lean). Autonomy A3, evidence V2. Erdős 165 — partial (Trellis) urn:qed:3d78fb043de4 2026-06-10T00:00:00Z Hefty, Horn, King and Pfender (2025). Autonomy A1, evidence V1. Erdős Problem 90: The unit distance problem — full (GPT-5.5 Pro) urn:qed:efc432a4d6b5 2026-06-09T00:00:00Z Improved explicit bound. Autonomy A1, evidence V1. Erdős Problem 619 — full (Claude Fable 5, Codex, GPT-5.5) urn:qed:0cdf5f2fa83e 2026-06-09T00:00:00Z Full solution (Lean). Autonomy A3, evidence V2. Erdős Problem 931 — partial (Claude, GPT-5.4) urn:qed:28d3692204d9 2026-06-08T00:00:00Z Partial result. Autonomy A1, evidence V1. Erdős Problem 927 — full (Aristotle) urn:qed:1ed487c42d82 2026-06-05T00:00:00Z Spencer (1971). Autonomy A1, evidence V1. Erdős 696 — full (Aristotle, Claude Code, Claude Opus 4.7, GPT-5.5 Pro) urn:qed:77ca53fbdade 2026-06-05T00:00:00Z Full solution (Lean). Autonomy A1, evidence V2. Erdős Problem 694 — full (Aristotle, Claude Code, Claude Opus 4.7, GPT-5.5 Pro) urn:qed:3d09fed8df1b 2026-06-05T00:00:00Z GPT-5.5 Pro (2026). Autonomy A1, evidence V1. Erdős Problem 623 — candidate (GPT-5.5 Pro) urn:qed:524b64d372a0 2026-06-04T00:00:00Z Candidate full solution. Autonomy A1, evidence V0. Erdős Problem 52 — candidate (GPT-5.5) urn:qed:2c99a876d706 2026-06-04T00:00:00Z Candidate solution to variant problem. Autonomy A1, evidence V0. Erdős Problem 775 — full (Aristotle) urn:qed:8490c14a400e 2026-06-03T00:00:00Z Gao (2025). Autonomy A1, evidence V3. Erdős Problem 762 — full (Aristotle, Claude Opus 4.7, GPT) urn:qed:edd98d1ca14a 2026-06-03T00:00:00Z Steiner (2024). Autonomy A1, evidence V3.