What was already known
Younis supplied the two-set construction and a modulus-65 instance with exponent about 0.768503.
AI involvement
JD Jones set the objective. Claude agents found the retained residue sets with a constraint solver and proved the bound in Lean. Younis supplied the earlier two-set digit method, and no independent human mathematical review of the new instance is documented.
Claude agents found the new admissible m=145 residue pair and proved its bound under Jones’s objective; the predecessor construction is credited to Younis.
Importance
Improves the explicit lower-bound exponent for this nonlinear additive configuration.
Limitations
The proof does not show that the new residue sets are optimal or give a matching upper bound. The source’s literature search for later stronger bounds was limited.
Technical verification
The source reports Lean kernel proofs of the admissibility and exact exponent comparison, a transitive axiom audit and a separate 51-check Python enumeration. Comparator and NanoDa reproduction instructions are given, but completion of those external replays at this exact pin is not asserted here.
Formal checking
compiled proofs, kernel decide for finite checks, exact integer-power inequalities, transitive axiom audit
- Checker
- Lean kernel and project axiom audit
- Scope
- The m=145 residue admissibility, lower bound and exponent comparison in five selected statements
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The explanatory proof and reviews are AI-authored; no named human explanation of the new residue construction or independent mathematical review is documented. This is an evidence-gap default.
Correction and publication history
Improves the explicit lower-bound exponent for this nonlinear additive configuration.
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