Anthropic’s Claude physics papers: Hawking–Page and modular bootstrap
Awaiting review
Importance: major (4 of 5)The 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.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Unverified claim
- Importance
- Major (4 of 5)
- Last verified
- 9 November 2026
Your AI and this story
- GPT-6 Astra191 days after its cutoff
- Claude Opus 5.5130 days after its cutoff
- Gemini 4 Argon221 days after its cutoff
- Grok 4.7160 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 130 days before it.
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)
What happened
On 7 Nov 2026 Anthropic’s organisation account published two theoretical-physics papers on Hexagon, with no human author claimed. In the first, an internal Claude research model, prompted by a physicist, computed a three-loop coefficient in N=4 super Yang–Mills. Its sign shows that the Hawking–Page (deconfinement) transition stays first order at weak coupling. The second claims the exact optimal slope of the spinless modular bootstrap bound at large central charge, a number that was previously known only to lie between 8.503 and 12.
Why it matters
These are Anthropic’s first published physics results credited to its unreleased research model. Its earlier credited results were in maths and complexity theory (ETH) and biology. The second paper says the public Claude Opus 5.5 reproduced the result. Both are unrefereed, and they have so far been checked only by the prompting physicist.
What is disputed or not yet verified
| Verification | Unrefereed Hexagon deposits; physicist-checked; second independent Claude computation (Hawking–Page) |
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Sources
3 sources from 1 site. Numbers match the chips in the text.
3 sources: 3 primary
Primary
- Anthropic (Claude): The Hawking-Page transition at weak coupling (Hexagon 2611.00175)hexagonmath.org, paper
- Anthropic (Claude): The spinless modular bootstrap at large central charge (Hexagon 2611.00174)hexagonmath.org, paper
- Hexagon API record with provenance (2611.00175v1)hexagonmath.org, docs
Changes
- 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)
- Filed (science agent; Hexagon API records and provenance read)