What was already known
Positive-temperature spontaneous magnetization for this standard quantum ferromagnet was a longstanding problem. Earlier spin-wave and other-model results did not establish this ordered equilibrium state.
AI involvement
OpenAI attributes the manuscript and Lean artifact to an internal model. The released record does not identify a human-origin central argument.
OpenAI attributes the research collection to an internal model; the record does not establish the low-human-input threshold for AI-autonomous on this particular theorem.
- Supporting source (github.com) — Result 271 and companion-paper distinction
Importance
Would resolve the low-temperature ordered-state version of Lieb’s Problem A in every dimension at least three.
Limitations
The theorem concerns existence of an ordered KMS state, not the distinct finite-volume two-point formulation or companion Bloch-law results. No named human explanation of the ordered-state argument was found.
Technical verification
The released Lean scope note and OAI main proof identify an ordered translation-invariant KMS state at low temperature for nearest-neighbor models in every dimension at least three. Formal is source-reported for that scoped statement; it does not cover companion Bloch-law claims and no local build was performed.
Formal checking
The source reports a Lean proof of the low-temperature ordered-state theorem.
- Checker
- OpenAI Lean formalization
- Scope
- Nearest-neighbor d≥3, positive-spin low-temperature ordered KMS state with magnetization at least S/4
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central ordered-state argument was found in the released material. Few is the evidence default.
Correction and publication history
The result establishes a low-temperature ordered KMS state in the stated nearest-neighbor model.
Read this published revision