{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/","md":"https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon","date":"2026-11-07","date_precision":"day","short_title":"Anthropic's Claude physics papers: Hawking–Page and modular bootstrap","deck":null,"takeaway":"Anthropic's own Hexagon account posted two 'primarily AI-generated' hep-th papers on 7 Nov: an internal Claude research model computed a three-loop coefficient unknown for two decades (b = −1.48×10⁻³ λ²), and found the optimal slope of the spinless modular bootstrap, later reproduced by public Claude Opus 5.5. A physicist checked the results.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Anthropic (Claude): The Hawking-Page transition at weak coupling (Hexagon 2611.00175)","url":"https://hexagonmath.org/abs/2611.00175","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Anthropic (Claude): The spinless modular bootstrap at large central charge (Hexagon 2611.00174)","url":"https://hexagonmath.org/abs/2611.00174","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":3,"title":"Hexagon API record with provenance (2611.00175v1)","url":"https://hexagonmath.org/api/v1/works/2611.00175v1","type":"docs","group":"primary","domain":"hexagonmath.org"}],"official":3,"filed":"2026-11-08","updated":"2026-11-09","orgs":["Anthropic"],"title":"Anthropic deposits two physics papers by Claude on Hexagon: Hawking–Page transition stays first order at weak coupling, and the exact large-c slope of the spinless modular bootstrap (Λ ≈ 9.1266)","summary":"On 7 Nov 2026 Anthropic, as an organisation account, published two papers on hexagonmath.org with no human author claimed. In 'The Hawking-Page transition at weak coupling' (2611.00175) an internal Claude research model computed the sign of the quartic Polyakov-loop coefficient in N=4 super Yang–Mills on S³, which decides that the transition stays first order. 'The spinless modular bootstrap at large central charge' (2611.00174) finds the optimal slope Λ_V = 12π²/(π²+4 arcsinh²1) ≈ 9.1266. In both, a physicist checked the results; neither is refereed or on arXiv.","key_facts":["Hawking–Page (2611.00175, 42 pp): b = −1.48×10⁻³ λ² at three loops, a number that 'to our knowledge, has not been computed in the two decades since' the 2003 proposal; 'The transition is first order', slightly below the Hagedorn temperature; it reproduces the known two-loop Hagedorn temperature","Provenance (2611.00175): 'An internal Claude research model, prompted by a physicist, obtained the result presented here. The physicist checked it against several known special cases. A separate Claude computation using a different method, not included here, gives the same result.' Declared: primarily AI-generated; some parts human-checked","Modular bootstrap (2611.00174, 131 pp): for unitary compact 2D CFTs with c > 1 and only Virasoro currents, the best slope in Δ₁ ≤ c/Λ was known to lie between 8.503 and 12; the paper claims it is exactly Λ_V ≈ 9.1266, with an explicit functional giving Δ₁ < c/Λ_V + 0.483 c^{1/3} + O(1)","Provenance (2611.00174): 'The main result was first obtained autonomously by an internal Claude research model. The publicly available Claude Opus 5.5 later obtained the same result independently. Claude then wrote this paper, following brief guidance from a physicist, who also checked every main result.'","Context: Anthropic's 'internal Claude research model' was earlier credited with the 3-SAT/ETH refutation (27 Oct) and the scorpion-toxin binders (20 Oct). No Anthropic blog post or physicist reaction found on 8 Nov (web search)"],"key_numbers":[],"tags":["physics","hep-th","ads-cft","conformal-field-theory","claude","claude-opus-5-5","hexagon","anthropic"],"science":{"field":"physics","subfield":"high-energy theory (AdS/CFT, conformal bootstrap)","problem":"Order of the weak-coupling Hawking–Page/deconfinement transition in N=4 SYM; optimal large-c spinless modular bootstrap bound","result":"b = −1.48×10⁻³ λ² (first-order transition); optimal slope Λ_V = 12π²/(π²+4 arcsinh²1) ≈ 9.1266","open_since":"","ai_system":["internal Claude research model","Claude Opus 5.5"],"human_role":"Autonomous AI result with a physicist prompting and checking","verification":{"key":"none","label":"Unverified claim","text":"Unrefereed Hexagon deposits; physicist-checked; second independent Claude computation (Hawking–Page)"},"status":"pending","shock":""},"body_md":"## What happened\n\nOn 7 Nov 2026 Anthropic's organisation account published two theoretical-physics papers on Hexagon, with no human author\nclaimed. In the first, an internal Claude research model, prompted by a physicist, computed a three-loop coefficient in N=4 super\nYang–Mills. Its sign shows that the Hawking–Page (deconfinement) transition stays first order at weak coupling. The second\nclaims the exact optimal slope of the spinless modular bootstrap bound at large central charge, a number that was previously\nknown only to lie between 8.503 and 12.\n\n## Why it matters\n\nThese are Anthropic's first published physics results credited to its unreleased research model. Its earlier credited results\nwere in maths and complexity theory (ETH) and biology. The second paper says the public Claude Opus 5.5 reproduced the result.\nBoth are unrefereed, and they have so far been checked only by the prompting physicist.","disputed":[{"label":"Verification","text":"Unrefereed Hexagon deposits; physicist-checked; second independent Claude computation (Hawking–Page)","sources":[]}],"related":[{"id":"2026-11-09-claude-fable-5-2-mythos-5-2","url":"https://postcutoff.com/e/2026-11-09-claude-fable-5-2-mythos-5-2/","date":"2026-11-09","date_precision":"day","short_title":"Anthropic releases Claude Fable 5.2 and Claude Mythos 5.2","deck":null,"takeaway":"A new frontier claim from Anthropic on coding, robotics and formal mathematics at a lower price, and the clearest public statement so far of how close a lab's own measurements put it to its automated-AI-R&D threshold.","category":"model-release","category_label":"Model releases","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":8,"official":7,"filed":"2026-11-09","updated":"2026-11-09","orgs":["Anthropic"]},{"id":"2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential","url":"https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/","date":"2026-10-27","date_precision":"day","short_title":"Anthropic's Claude also refutes ETH","deck":null,"takeaway":"Hours after OpenAI's ETH announcement, Anthropic posted 'A 2^o(n) Time Algorithm for 3-SAT', credited to Claude. It is a deterministic #k-SAT algorithm built on tensor-network contraction, with a different approach from OpenAI's paper, a near-identical bound and a Lean 4 proof that uses only the standard axioms. The paper says the core algorithm was found on 16 Oct with 14M output tokens and no human input. OpenAI reports its model found its disproof that same day. Neither proof has had expert review.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":10,"official":8,"filed":"2026-10-27","updated":"2026-11-06","orgs":["Anthropic"]},{"id":"2026-10-20-claude-scorpion-toxin-binders","url":"https://postcutoff.com/e/2026-10-20-claude-scorpion-toxin-binders/","date":"2026-10-20","date_precision":"day","short_title":"Claude designs binders against scorpion neurotoxins","deck":null,"takeaway":"It is one of the first published cases of a frontier lab's model running a wet-lab-validated design campaign mostly by itself, with data released for checking.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":2,"official":2,"filed":"2026-10-21","updated":"2026-10-21","orgs":["Anthropic","Citrini Research"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-09","type":"edit","text":"Anthropic's Fable 5.2 announcement attributes both results to Claude Fable 5.2 (the 'internal Claude research model' was Fable 5.2 before release)"},{"date":"2026-11-08","type":"filed","text":"Created (science agent; Hexagon API records and provenance read)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-08","run":null,"sources_read":"Science agent; Hexagon API records and provenance read","updated":"2026-11-09","human_review":null,"version":{"date":"2026-11-09"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":191,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":130,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":221,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":160,"in_training_data":false}],"short_url":"https://postcutoff.com/s/anthropic-claude-physics-papers"}