---
id: "2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon"
url: "https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/"
as_of: "2026-11-09T21:13:00+01:00"
date: "2026-11-07"
date_precision: day
category: science
importance: 4
confidence: medium
status: [Awaiting review]
verification: Unverified claim
sources: 3
editor: human editor
human_review: null
version: "2026-11-09"
---

As of: 2026-11-09 21:13 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-11-07-anthropic-claude-hawking-page-modular-bootstrap-hexagon/

# Anthropic's Claude physics papers: Hawking–Page and modular bootstrap

Full 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)

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)

## 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)

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 191 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 130 days after its cutoff
- Gemini 4 Argon (training cutoff March 2026): 221 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 160 days after its cutoff

## Sources

1. [Anthropic (Claude): The Hawking-Page transition at weak coupling (Hexagon 2611.00175)](https://hexagonmath.org/abs/2611.00175) (hexagonmath.org, paper)
2. [Anthropic (Claude): The spinless modular bootstrap at large central charge (Hexagon 2611.00174)](https://hexagonmath.org/abs/2611.00174) (hexagonmath.org, paper)
3. [Hexagon API record with provenance (2611.00175v1)](https://hexagonmath.org/api/v1/works/2611.00175v1) (hexagonmath.org, docs)

## Changes

- 2026-11-09: 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)
- 2026-11-08 (filed): Created (science agent; Hexagon API records and provenance read)

## Related

- 2026-11-09: [Anthropic releases Claude Fable 5.2 and Claude Mythos 5.2](https://postcutoff.com/e/2026-11-09-claude-fable-5-2-mythos-5-2/index.md)
- 2026-10-27: [Anthropic's Claude also refutes ETH](https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/index.md)
- 2026-10-20: [Claude designs binders against scorpion neurotoxins](https://postcutoff.com/e/2026-10-20-claude-scorpion-toxin-binders/index.md)