What was already known
Myers conjectured the formula, and earlier work bounded R(c) between 40c+41 and 44c+45. A previous Claude result covered c+1 divisible by 3, 4, 5 or 7 and some individual values.
AI involvement
The submitter credits Claude Fable 5 with the new spoke relaxation, proof, Lean reduction and SAT computations under human operational direction. A complete interaction transcript is unavailable.
The source credits Claude with the central new spoke construction and proof; autonomy beyond the stated operational direction is not independently documented.
Importance
Claims the remaining general case of a specialist four-color Rado conjecture.
Limitations
c=0 and c=1 are exceptions. The repository reports Lean reduction and DRAT checks, but the large DRAT proof files are hash-pinned rather than shipped, and no human mathematician has reviewed the bridge from templates to the intended statement.
Technical verification
The repository reports DRAT-checked unsatisfiability of both finite templates, exact base-case checks, and a Lean 4 conditional reduction with a template hash bridge. This is a reported machine check of the full claim chain, not rerun here; human proof review is absent.
Formal checking
Lean proof and regenerated-template hash check
- Checker
- Lean 4 kernel via Rado.lean and verify.sh
- Scope
- Conditional universal reduction from two template UNSAT facts and R(2)=121 to R(c)=40c+41 for all c>=2
- Basis
- Reported by the linked checker
Formal checking
Exact SAT solves and DRAT verification; separate encoder and finite-case checks
- Checker
- kissat and drat-trim, with independent encoder and solver cross-checks
- Scope
- UNSAT of M(3,1,1) and M(3,2,2) and required finite base values
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Default for missing human explanation: the supplied proof describes the spoke mechanism, but the repository explicitly reports no human mathematical review or explanation.
Correction and publication history
Claims the remaining general case of a specialist four-color Rado conjecture.
Read this published revision