What was already known
JD Jones’s note had already stated and proved the border theorems. Goethals–Seidel constructions, other border cases, and Hadamard matrices of orders 20 and 52 were known before this formalization.
AI involvement
Jones supplied the source note and selected the scope. Claude Fable and Opus agents chose the alternative proof route and formalized it; Jones says he did not mathematically review that derivation.
Claude supplied a distinct central mathematical derivation of the already stated Theorem D clauses; the theorem statement and prior proof came from Jones.
Importance
Adds a machine-checked alternative derivation for a bounded part of an existing theorem package.
Limitations
The formal check does not cover the source note’s whole Hadamard program. No independent human mathematician comparison with Jones’s proof is documented, and the protected multi-kernel comparison was not reported for this code version.
Technical verification
The cited disclosure reports a successful local Lean build and transitive axiom audit for the 26 compared theorems. This checks the formal integer route on the stated clauses, not the unformalized Theorem C clauses, census, or source-fidelity/priority claims. Comparator and NanoDa had not run at this commit.
Independent checking
Local build, kernel proof checking, and transitive audit limited to standard Lean axioms
- Checker
- Lean 4 kernel and project axiom-audit script
- Scope
- The 26 compared formal statements, including Theorem D clauses D-a through D-e
- Basis
- Reported by the linked checker
Human understanding
Default for missing human explanation of the alternative integer proof: Jones disclaims mathematical work on the formalization and reports only AI reviews.
Correction and publication history
Adds a machine-checked alternative derivation for a bounded part of an existing theorem package.
Read this published revision