Claude Derives Sharp Large-c Bootstrap Bound

The compelling story is not “AI solved quantum gravity,” but that Claude produced a precise, testable limit for a technically mature mathematical method. Its significance depends on independent verification of the proof and computer-assisted attainment checks.

• –Tightens the known large-central-charge slope range from roughly 8.503–12 to ΛV ≈ 9.1266.
• –Uses an electrostatic potential and zero-distribution framework to characterize asymptotically optimal functionals.
• –Applies only to spinless modular S-invariance at zero angular potential, not the full spinful bootstrap or pure-gravity spectrum.
• –Does not prove that conformal field theories saturating the bound exist.
• –The leading result is presented as proved, while finer correction terms remain conjectural and numerical thresholds are not fully computed. [State of Proof review](https://stateofproof.org/paper-watch/hexagon-2611-00174)