What was already known
Earlier all-observable spectral-gap results covered smaller temperature ranges. Full β<1 covariance bounds controlled linear observables, not this Poincaré inequality.
AI involvement
OpenAI credits the manuscript to its internal-model mathematical research collection. The release does not establish autonomy for this specific result.
OpenAI's institutional AI authorship and production account support AI-led mathematical work, without establishing fully autonomous task choice.
Importance
Extends the all-observable spectral-gap bound through the fixed high-temperature phase at zero field.
Limitations
The constant may depend on fixed β. The claim excludes external field and β=1; the Lean project was not locally rebuilt, and no named human proof check is documented.
Technical verification
The repository's Lean 4 theorem OAI.SKGap.sk_main proves the fixed-beta zero-field Poincaré and discrete-gap statements; the scope note maps it to the manuscript. This is a source-reported machine check, not a local build.
Formal checking
Lean proof in OAI/Probability/SKGap/Main.lean matched against the SKHighTemperature comparator and scope note
- Checker
- Lean kernel via OAI.SKGap.sk_main
- Scope
- For each fixed 0<beta<1, a disorder-high-probability all-observable Poincaré inequality and discrete heat-bath gap at least 1/(C_beta n) at zero field
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Default for missing human-understanding evidence: the manuscript explains a proof mechanism, but no named human account of understanding this model-produced argument was found.
Correction and publication history
Extends the all-observable spectral-gap bound through the fixed high-temperature phase at zero field.
Read this published revision