What was already known
Entropy and Landau-nullspace tools were classical; earlier work did not give this static classification of the coupled system under these hypotheses.
AI involvement
Gemini DeepThink supplied the natural-language proof; Claude Code and Aristotle developed its Lean formalization. Ilin posed the question, checked the proof by hand, supervised the formalization and compared it with the intended physics.
Gemini supplied the complete proof blueprint and AI tools supplied the formalization, with substantial human supervision and statement alignment.
Importance
The work gives a new equilibrium classification within explicit regularity and score assumptions.
Limitations
The polynomial score bound is an extra hypothesis, so the theorem does not classify all physical equilibria. The author cautions that other definition mismatches may remain.
Technical verification
Ilin reports a complete hand check of Gemini’s argument and a Lean kernel check of the stated 12-hypothesis theorem; the rating applies to that theorem, not all physically possible equilibria.
Formal checking
Hand verification of the six-step proof, including checking cited supporting theorems
- Checker
- Vasily Ilin
- Scope
- Gemini’s natural-language equilibrium argument
- Basis
- Reported by the linked checker
Formal checking
Complete reported Lean build with zero sorrys
- Checker
- Lean 4 kernel; Claude Code/Aristotle development
- Scope
- CoulombConcreteTheorem42 under positivity, smoothness, Schwartz decay, polynomial score bound and steady equations
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Ilin describes and checks the proof architecture from entropy dissipation through polynomial matching, Ampère/Gauss closure and harmonic magnetic field.
Correction and publication history
The work gives a new equilibrium classification within explicit regularity and score assumptions.
Read this published revision