{"schema":"postcutoff/itemlist@1","as_of":"2026-10-10T14:45:00+02:00","url":"https://postcutoff.com/news/science/","md":"https://postcutoff.com/news/science/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"Adam Bicz","policy":"https://postcutoff.com/about/"},"license":null,"item_type":"Event","scope":"science","page":1,"pages":4,"total":199,"per_page":50,"feed":"https://postcutoff.com/feeds/science.xml","items":[{"id":"2026-10-08-hyperkahler-syz-conjecture-engel-mauri","url":"https://postcutoff.com/e/2026-10-08-hyperkahler-syz-conjecture-engel-mauri/","date":"2026-10-08","date_precision":"day","short_title":"Engel & Mauri post a 7-page proof of the hyperkähler SYZ conjecture, two days after OpenAI's catalogue claimed it; AI used only to proofread","deck":null,"takeaway":"The hyperkähler SYZ conjecture (every nef line bundle on a compact hyperkähler manifold is semiample) has a human-written proof by Philip Engel and Mirko Mauri, which also gives finitely many deformation classes in each dimension when b2 ≥ 5. OpenAI's catalogue claimed the same theorem on 6 Oct; the authors say the proof structures 'appear similar'.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-09","updated":"2026-10-09","orgs":["University of Illinois Chicago","Université Paris Cité","OpenAI"]},{"id":"2026-10-08-dualization-eth-lower-bound-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-08-dualization-eth-lower-bound-gpt-6-astra/","date":"2026-10-08","date_precision":"day","short_title":"GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETH","deck":null,"takeaway":"Whether monotone Boolean dualization, equivalently enumerating all minimal transversals of a hypergraph, can be done in output-polynomial time has been open since the 1990s. A short preprint says no, assuming the Exponential Time Hypothesis, and its authors say the proof 'was originally discovered by GPT-6 Astra'.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-09","updated":"2026-10-09","orgs":["Hokkaido University","Okayama University","Hosei University","OpenAI"]},{"id":"2026-10-08-karagila-openai-partition-principle","url":"https://postcutoff.com/e/2026-10-08-karagila-openai-partition-principle/","date":"2026-10-08","date_precision":"day","short_title":"Set theorist Asaf Karagila refuses to review OpenAI's claimed solution of the Partition Principle problem (does PP imply AC?): 'It sucked'; calls the 722-paper release a 'Denial of Service'","deck":null,"takeaway":"OpenAI's catalogue claims the Partition Principle does not imply the Axiom of Choice, one of set theory's oldest open problems (Russell, 1906), with a partial Lean formalization. The best-known expert on the problem, who had promised a bottle of whisky for a solution, called the paper unreadable and declined to check it.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":5,"official":3,"filed":"2026-10-09","updated":"2026-10-09","orgs":["OpenAI"]},{"id":"2026-10-08-hilbert-number-lower-bound-gpt-5-6-sol-lean","url":"https://postcutoff.com/e/2026-10-08-hilbert-number-lower-bound-gpt-5-6-sol-lean/","date":"2026-10-08","date_precision":"day","short_title":"Hilbert's 16th problem","deck":"Qin & Sun prove H(d) = Ω(d² ln² d), the first log-factor gain since 1995, with GPT-5.6 Sol developing the proof and a Lean 4 certificate","takeaway":"The lower bound for the number of limit cycles of degree-d planar polynomial vector fields improves from d² ln d to d² ln² d. The authors say GPT-5.6 Sol developed the proof strategy and arguments, and the construction is formalized in Lean 4.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-09","updated":"2026-10-09","orgs":["Chinese Academy of Sciences","OpenAI"]},{"id":"2026-10-08-antiquity-ai-archive-search-meteorite-rhinos","url":"https://postcutoff.com/e/2026-10-08-antiquity-ai-archive-search-meteorite-rhinos/","date":"2026-10-08","date_precision":"day","short_title":"AI archive search finds forgotten meteorite and eruptions","deck":null,"takeaway":"It shows how cheap models make it practical for one person to read whole archives (one filtering pass cost about $3), and it produces the kind of result catalogue maintainers can check against the cited pages.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-10","updated":"2026-10-10","orgs":["Anthropic","TypeSafe AI"]},{"id":"2026-10-08-claude-science-complete-uv-sky-map","url":"https://postcutoff.com/e/2026-10-08-claude-science-complete-uv-sky-map/","date":"2026-10-08","date_precision":"day","short_title":"Claude Science builds a complete ultraviolet map of the sky","deck":null,"takeaway":"It is a small but concrete example of agentic AI doing the data-heavy \"infrastructure\" work that scientists often postpone for years.","category":"science","category_label":"Science & math","importance":2,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-09","updated":"2026-10-09","orgs":["Anthropic","Johns Hopkins University"]},{"id":"2026-10-07-colkitt-codex-integer-multiplication-exponent","url":"https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/","date":"2026-10-07","date_precision":"day","short_title":"Outside researchers using AI crowdsource a tighter exponent in OpenAI's integer-multiplication result #109, from 2^-182 to above 2^-14 (conditional)","deck":null,"takeaway":"In a parallel repository Swapnil Jain (@SJ_Swapnil_Jain, with Claude) posted seven rounds ending at κ ≈ 6.40×10^-5 (> 2^-14) on the evening of 8 Oct, the highest claimed value.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":20,"official":6,"filed":"2026-10-07","updated":"2026-10-08","orgs":["Independent researchers","OpenAI"]},{"id":"2026-10-07-exact-overlaps-conjecture-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-07-exact-overlaps-conjecture-gpt-6-astra/","date":"2026-10-07","date_precision":"day","short_title":"Exact overlaps conjecture for self-similar measures on the line proved","deck":"GPT-6 Astra found the first proof (Kittle & Kogler), 47,000-line Lean formalization; OpenAI's catalogue claims it independently","takeaway":"A central conjecture of fractal geometry, open in general since Hochman's 2014 breakthrough, now has a proof whose key part came from a GPT-6 Astra session. The authors rewrote and formalized it in Lean, and OpenAI's own release claims the same theorem.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":5,"official":5,"filed":"2026-10-08","updated":"2026-10-08","orgs":["University College London","Institute for Advanced Study","OpenAI"]},{"id":"2026-10-07-lebrun-salamon-conjecture-proof","url":"https://postcutoff.com/e/2026-10-07-lebrun-salamon-conjecture-proof/","date":"2026-10-07","date_precision":"day","short_title":"Two claimed proofs of the LeBrun–Salamon conjecture","deck":"Hu, Liu & Wan (arXiv, ChatGPT as 'auxiliary tool') and OpenAI's catalogue (family 062)","takeaway":"The 1994 conjecture that every positive quaternion-Kähler manifold is a symmetric Wolf space now has two independent claimed proofs, one by human geometers who used ChatGPT and one in OpenAI's AI-generated catalogue. Neither has been refereed.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":4,"official":4,"filed":"2026-10-08","updated":"2026-10-08","orgs":["Chongqing University of Technology","OpenAI"]},{"id":"2026-10-07-multiple-unicast-conjecture-false-gpt-6","url":"https://postcutoff.com/e/2026-10-07-multiple-unicast-conjecture-false-gpt-6/","date":"2026-10-07","date_precision":"day","short_title":"Braverman & He refute the 2004 undirected multiple-unicast (network coding) conjecture with a GPT-6-found counterexample on PG(2, 9)","deck":null,"takeaway":"A 22-year-old network coding conjecture is false: on undirected networks, coding can beat routing. The counterexample came from GPT-6, and the Princeton authors checked it with a standalone symbolic verifier.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-08","updated":"2026-10-08","orgs":["Princeton University","OpenAI"]},{"id":"2026-10-07-virtual-biology-initiative-1-8b-doe-nih-deepmind-meta","url":"https://postcutoff.com/e/2026-10-07-virtual-biology-initiative-1-8b-doe-nih-deepmind-meta/","date":"2026-10-07","date_precision":"day","short_title":"Biohub's Virtual Biology Initiative grows to $1.8B","deck":"DOE, NIH, Google DeepMind, Isomorphic Labs and Meta join the push for open data to build AI 'virtual cells'","takeaway":"Virtual-cell models need far more standardized perturbation data than exists.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":2,"official":1,"filed":"2026-10-08","updated":"2026-10-08","orgs":["Biohub","US Department of Energy","National Institutes of Health","Google DeepMind","Isomorphic Labs","Meta"]},{"id":"2026-10-07-ai-for-math-fund-2026-grants","url":"https://postcutoff.com/e/2026-10-07-ai-for-math-fund-2026-grants/","date":"2026-10-07","date_precision":"day","short_title":"AI for Math Fund names 22 new grants","deck":"Total commitment reported at $35.1M","takeaway":"The AI for Math Fund, run by Renaissance Philanthropy with XTX Markets as founding donor, announced 22 new grants in early October 2026.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"partly","labels":["Partly confirmed"]},"sources":2,"official":1,"filed":"2026-10-09","updated":"2026-10-09","orgs":["Renaissance Philanthropy","XTX Markets"]},{"id":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":63,"official":13,"filed":"2026-10-07","updated":"2026-10-10","orgs":["OpenAI"]},{"id":"2026-10-06-quasi-riemann-hypothesis-openai","url":"https://postcutoff.com/e/2026-10-06-quasi-riemann-hypothesis-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI model claims the quasi-Riemann hypothesis","deck":"No zeta or Dirichlet L-function zeros with Re s > 7/8, and no Landau–Siegel zeros (Lean-formalized)","takeaway":"If correct, this is the largest advance on the zeros of ζ since the 19th century, and it would remove the Siegel-zero obstruction that runs through modern analytic number theory.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":6,"filed":"2026-10-07","updated":"2026-10-09","orgs":["OpenAI"]},{"id":"2026-10-06-unique-games-conjecture-openai","url":"https://postcutoff.com/e/2026-10-06-unique-games-conjecture-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI model claims a proof of Khot's Unique Games Conjecture, with Lean formalization","deck":null,"takeaway":"If OpenAI's claimed proof holds, it settles the Unique Games Conjecture, a central open problem in hardness of approximation since 2002. It comes with a Lean formalization, but experts have not yet checked it.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-10-07","updated":"2026-10-09","orgs":["OpenAI"]},{"id":"2026-10-06-hodge-conjecture-cm-abelian-varieties-openai","url":"https://postcutoff.com/e/2026-10-06-hodge-conjecture-cm-abelian-varieties-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI release claims the rational Hodge conjecture for all CM abelian varieties, which would give the Tate conjecture for abelian varieties over finite fields (no Lean proof)","deck":null,"takeaway":"Family 032 of OpenAI's 6 Oct 2026 math release claims the rational Hodge conjecture for every complex abelian variety with complex multiplication, in every dimension and codimension.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":4,"filed":"2026-10-07","updated":"2026-10-08","orgs":["OpenAI"]},{"id":"2026-10-06-free-group-factors-isomorphism-openai","url":"https://postcutoff.com/e/2026-10-06-free-group-factors-isomorphism-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI model claims the free group factor problem","deck":"L(F₂) ≅ L(F₃), so all free group factors are isomorphic (Lean-formalized)","takeaway":"The problem has been one of the best-known open questions in operator algebras for decades.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-07","updated":"2026-10-07","orgs":["OpenAI"]},{"id":"2026-10-06-artin-davenport-cubic-forms-ten-variables","url":"https://postcutoff.com/e/2026-10-06-artin-davenport-cubic-forms-ten-variables/","date":"2026-10-06","date_precision":"day","short_title":"Artin–Davenport conjecture proved","deck":"Every integral cubic form in 10+ variables has a nontrivial zero (Bonolis, Browning, Glas, Wang; key lemma via ChatGPT 6.0, Codex Lean auto-formalisation)","takeaway":"This is one of the oldest benchmark problems of the circle method, and a well-known group of analytic number theorists has now claimed it in full, at the sharp number of variables.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-07","updated":"2026-10-07","orgs":["TU Graz","ISTA","Imperial College London","Leibniz Universität Hannover","Academia Sinica","OpenAI"]},{"id":"2026-10-06-gch-above-strongly-compact-woodin-question","url":"https://postcutoff.com/e/2026-10-06-gch-above-strongly-compact-woodin-question/","date":"2026-10-06","date_precision":"day","short_title":"Woodin's question answered","deck":"GCH below a strongly compact cardinal implies GCH everywhere (Zhixing You, 4-page proof with GPT-6 Astra)","takeaway":"Woodin's question is a well-known open problem about large cardinals and the continuum function, and a short positive answer would be a notable result in set theory.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-07","updated":"2026-10-07","orgs":["Hebrew University of Jerusalem","OpenAI"]},{"id":"2026-10-06-finite-index-over-treeable-jkl-problem","url":"https://postcutoff.com/e/2026-10-06-finite-index-over-treeable-jkl-problem/","date":"2026-10-06","date_precision":"day","short_title":"Chen, Tserunyan & Tucker-Drob solve the Jackson–Kechris–Louveau 'finite index over treeable' problem (2002); ChatGPT 6 Astra Ultra supplied a 'crucial observation'","deck":null,"takeaway":"A countable Borel equivalence relation that contains a treeable subrelation of finite index is itself treeable. This answers Open Problem 6.4(B) of Jackson–Kechris–Louveau (2002), open even in the index-2 measure-preserving case. The authors had the strategy; GPT supplied the observation that made the stages fit together.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-09","updated":"2026-10-09","orgs":["University of Warsaw","McGill University","University of Florida","OpenAI"]},{"id":"2026-10-06-eleven-square-packing-optimality-lean","url":"https://postcutoff.com/e/2026-10-06-eleven-square-packing-optimality-lean/","date":"2026-10-06","date_precision":"day","short_title":"Walter Trump's 1979 packing of 11 unit squares proved optimal, with a full Lean verification (AI involvement reported, unconfirmed)","deck":null,"takeaway":"It settles a well-known open case in packing theory, widely known from xkcd.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":5,"filed":"2026-10-07","updated":"2026-10-07","orgs":["Open-source community"]},{"id":"2026-10-06-polynomial-littlewood-offord-gpt-6-pro","url":"https://postcutoff.com/e/2026-10-06-polynomial-littlewood-offord-gpt-6-pro/","date":"2026-10-06","date_precision":"day","short_title":"Optimal bound for the polynomial Littlewood–Offord problem, 'discovered autonomously by GPT-6 Pro' (exposition by Grebennikov)","deck":null,"takeaway":"It is another case where a consumer-tier model (ChatGPT's GPT-6 Pro) is credited with the whole idea behind an optimal bound in a well-studied area, with a public transcript.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":2,"official":1,"filed":"2026-10-07","updated":"2026-10-07","orgs":["OpenAI"]},{"id":"2026-10-05-claude-refutes-3sum-apsp-hypotheses","url":"https://postcutoff.com/e/2026-10-05-claude-refutes-3sum-apsp-hypotheses/","date":"2026-10-05","date_precision":"day","short_title":"Claude discovers an algorithm that refutes the 3SUM and APSP hypotheses","deck":"Truly subquadratic 3SUM and truly subcubic APSP (Alman & Vassilevska Williams, Lean-verified)","takeaway":null,"category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":4,"official":3,"filed":"2026-10-06","updated":"2026-10-10","orgs":["Anthropic","Columbia University","MIT"]},{"id":"2026-10-05-deepmind-alphaprotein-novo-enzyme-design","url":"https://postcutoff.com/e/2026-10-05-deepmind-alphaprotein-novo-enzyme-design/","date":"2026-10-05","date_precision":"day","short_title":"Google DeepMind's AlphaProtein Novo designs new-to-nature enzymes from scratch (piperidine synthesis, DEHP degradation), with Frances Arnold's lab","deck":null,"takeaway":"Most industrial enzymes start from natural proteins and are improved by mutation.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":5,"official":4,"filed":"2026-10-06","updated":"2026-10-07","orgs":["Google DeepMind","Caltech","University of Pittsburgh"]},{"id":"2026-10-04-linear-hadwiger-conjecture-proved-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-04-linear-hadwiger-conjecture-proved-gpt-6-astra/","date":"2026-10-04","date_precision":"day","short_title":"Linear Hadwiger conjecture proved","deck":"K_t-minor-free graphs are O(t)-colourable; proof found by GPT-6 Astra (Norin & Steiner), Lean-verified by Codex","takeaway":"With the 3SUM/APSP refutation and the KLS proofs posted the same week, it marks a step change in AI-originated mathematics: famous problems now fall with proofs largely written by models and checked by machines.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-06","updated":"2026-10-06","orgs":["OpenAI","McGill University","ETH Zurich"]},{"id":"2026-10-02-kls-conjecture-proved-ai-assisted","url":"https://postcutoff.com/e/2026-10-02-kls-conjecture-proved-ai-assisted/","date":"2026-10-02","date_precision":"day","short_title":"Kannan–Lovász–Simonovits conjecture proved in two AI-assisted preprints","deck":"Song–Zhang's O(1) bound, then Bizeul–Klartag–Lehec ('most proofs … found by ChatGPT')","takeaway":"KLS was among the best-known open problems in high-dimensional geometry, with consequences for sampling algorithms on convex bodies.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":2,"filed":"2026-10-06","updated":"2026-10-06","orgs":["Microsoft Research","Weizmann Institute of Science","OpenAI","Anthropic"]},{"id":"2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe","url":"https://postcutoff.com/e/2026-10-02-epsilon-dvoretzky-conjecture-klartag-moshe/","date":"2026-10-02","date_precision":"day","short_title":"Klartag and Moshe prove the ε-Dvoretzky conjecture","deck":"The key probabilistic idea came from a ChatGPT discussion","takeaway":"This is a classical problem in asymptotic geometric analysis, and the preprint comes from Boaz Klartag (Tel Aviv University and Weizmann Institute), a leading researcher in the field.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-05","updated":"2026-10-05","orgs":["Tel Aviv University","Weizmann Institute of Science","OpenAI"]},{"id":"2026-10-02-meta-muse-spark-six-math-papers","url":"https://postcutoff.com/e/2026-10-02-meta-muse-spark-six-math-papers/","date":"2026-10-02","date_precision":"day","short_title":"Meta publishes six maths papers made by mathematicians working with Muse Spark in ordinary meta.ai chat, saying five answer open questions","deck":null,"takeaway":"It adds Meta to the labs with AI-for-math research claims, and it shows how crowded the field has become: the same open problems are now often solved independently by several AI-assisted teams within weeks.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":8,"filed":"2026-10-03","updated":"2026-10-07","orgs":["Meta"]},{"id":"2026-10-02-tomon-triangle-free-box-graphs-astra","url":"https://postcutoff.com/e/2026-10-02-tomon-triangle-free-box-graphs-astra/","date":"2026-10-02","date_precision":"day","short_title":"ChatGPT Astra finds geometric triangle-free graphs with near-optimal chromatic number, the first improvement on Burling's 1965 box bound","deck":null,"takeaway":"This is an exponential improvement on a 60-year-old bound in geometric graph colouring, and it is another case where the model supplied the constructions rather than routine checks.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-05","updated":"2026-10-05","orgs":["Umeå University","OpenAI"]},{"id":"2026-10-01-lehmer-permutation-conjecture-opus-5-5","url":"https://postcutoff.com/e/2026-10-01-lehmer-permutation-conjecture-opus-5-5/","date":"2026-10-01","date_precision":"day","short_title":"Lehmer's 1965 permutation conjecture proved","deck":"Claude Opus 5.5 found the short hypercube proof","takeaway":"This is a famous, decades-old combinatorics problem named in Knuth's TAOCP, and the paper credits the key proof idea directly to Claude Opus 5.5.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":1,"filed":"2026-10-02","updated":"2026-10-09","orgs":["Eindhoven University of Technology","Anthropic","Harmonic"]},{"id":"2026-10-01-bootloops-claude-shaped-science","url":"https://postcutoff.com/e/2026-10-01-bootloops-claude-shaped-science/","date":"2026-10-01","date_precision":"day","short_title":"Harvard physicist Matthew Schwartz releases BootLoops, an open-source harness that let Claude produce 36 manuscripts in 18 fields in three months","deck":null,"takeaway":"It is one of the broadest demonstrations so far of a single researcher using an AI agent to work across many unrelated fields, with code released openly.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":5,"official":4,"filed":"2026-10-05","updated":"2026-10-05","orgs":["Harvard University","Anthropic"]},{"id":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":9,"official":4,"filed":"2026-09-30","updated":"2026-10-09","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]},{"id":"2026-09-30-barvinok-log-concavity-totally-unimodular-astra","url":"https://postcutoff.com/e/2026-09-30-barvinok-log-concavity-totally-unimodular-astra/","date":"2026-09-30","date_precision":"day","short_title":"GPT-6 Astra proves Barvinok's log-concavity question for contingency tables on lines, giving lattice-point bounds for all totally unimodular polytopes","deck":null,"takeaway":"It is a named question in a central area of combinatorial counting, with the core proof credited to the model.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting 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