What was already known
Earlier rigorous results covered high temperature and a large-component regime; the all-temperature spin-decay case remained open.
AI involvement
OpenAI credits an internal model with the manuscript and formalization. The record does not establish autonomous origin for this particular argument.
The institution credited as author and the release’s internal-model production account support AI-led involvement.
Importance
Establishes the stated all-temperature exponential spin-correlation decay for n≥3.
Limitations
The Lean result concerns finite-volume spin correlations. It does not establish a full transfer-operator gap, fixed-boundary claim, Gibbs-state uniqueness or low-temperature asymptotics. No named human mathematical check or explanation is documented.
Technical verification
The Lean release scope and comparator match the finite free-boundary spin-correlation theorem, and Main.lean states the resulting ExponentialDecay theorem. The infinite-volume limit and full O(4) spectral gap are outside that formalization.
Formal checking
The Lean release scope and comparator match the finite free-boundary spin-correlation theorem, and Main.lean states the resulting ExponentialDecay theorem. The infinite-volume limit and full O(4) spectral gap are outside that formalization.
- Checker
- Lean 4/mathlib formalization in ClassicalON/Main.lean
- Scope
- Finite-volume exponential spin-correlation decay for n≥3, bounded nonnegative couplings and free boundary
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explains the fixed-target/cluster argument or its complete reasoning; Few is the evidence default.
Correction and publication history
Establishes the stated all-temperature exponential spin-correlation decay for n≥3.
Read this published revision