What was already known
Lüscher’s abelian construction and perturbative nonabelian results did not give this stated nonperturbative smooth local measure for the covered chiral theories. Craig proposed the refinement strategy; the proof compares projectors at successive lattice spacings and controls the resulting current and global phases.
AI involvement
Craig explicitly describes the result as an Astra-led proof after his refinement proposal and iterations with Astra and outside experts. Astra also carried out proposed tests and formalization. Craig revised the text; Golterman, Shamir and other named experts contributed questions and feedback. The archive’s subsequent proof-detail completions remain separately documented.
Importance
Addresses a longstanding obstruction to a nonperturbative lattice definition of the covered chiral gauge theories.
Limitations
Admissibility is an essential plaquette bound. Relative phases between components remain free; reflection positivity, practical simulation and an interacting continuum theory remain open. The checking report records a failed original Comparator reference comparison alongside successful separate kernel and statement-type checks; physical correspondence is not experimental confirmation.
Technical verification
Craig’s versioned supplement reports successful Lean 4.35.0-rc2 compilation of all 16 modules, standard-axiom checking and separate kernel replay of the exported proofs, with statement-type checks. The original Comparator command failed on generated-name/proof-body matching; separate proof checks passed. Source correspondence was reviewed by AI agents, rather than an independent human panel.
Formal checking
Craig’s versioned supplement reports successful Lean 4.35.0-rc2 compilation of all 16 modules, standard-axiom checking and separate kernel replay of the exported proofs, with statement-type checks. The original Comparator command failed on generated-name/proof-body matching; separate proof checks passed. Source correspondence was reviewed by AI agents, rather than an independent human panel.
- Checker
- Lean 4.35.0-rc2 and separate kernel/axiom checks reported by Nathaniel Craig
- Scope
- Theorem 4.1: smooth exponentially local gauge-covariant current and gauge-invariant measure for SU(5), R=10⊕5-bar, on each nonempty admissible component of a finite periodic four-dimensional lattice; stated Standard Model restrictions.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Craig’s initial refinement strategy and expert feedback are documented. The reviewed sources do not identify how completely a named human can explain the Astra-led analytic and global-integrability proof; Few is the documentation default, not a report that humans cannot understand it.
Correction and publication history
Added the sourced contribution with its stated hypotheses, AI role, prior work and checking limits.
Read this published revision