What was already known
Dimitrov posed the full-range inequalities and proved their k=1 cases; the source discusses k=2 and k=3 but not full-range proofs.
AI involvement
Mazur asked Codex to find and attempt recent open problems. The project credits Codex with selecting these targets, finding the reductions and writing the Lean proofs; Mazur directed and maintained the work.
Codex selected both conjectures and supplied their substantive mathematical reductions and Lean proofs under Mazur’s direction.
Importance
The proofs extend two stated inequalities to all parameters and identify their equality cases.
Limitations
The other conjectures in Dimitrov’s paper are outside this result. Historical first-proof priority has not been independently confirmed.
Technical verification
The cited repository reports a complete Lean/Mathlib proof of both full-range inequalities and equality cases, with no proof-library sorry or custom axiom. Its workflow reports exact Comparator matching, kernel and NanoDa checks; those are source-reported, not rerun here.
Formal checking
Lean build and trust-zero check, statement comparison, axiom audit and independent proof replay
- Checker
- Lean kernel, Comparator and NanoDa in Mazur’s reported workflow
- Scope
- Conjectures 1 and 3 for every k ≥ 1, n ≥ 2, plus equality iff n is prime
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No human explanation of the central full-range reductions or completed human proof review is documented. Mazur’s project decisions do not establish mathematical understanding; Few records the missing evidence.
Correction and publication history
The proofs extend two stated inequalities to all parameters and identify their equality cases.
Read this published revision