What was already known
Rigorous formulas for bounded log-potentials were previously confined to sufficiently small pattern density or other restricted regimes; hard-constraint capacity results concern a different zero-one potential model.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Removes the small-density restriction for the Gaussian Ising perceptron at positive temperature.
Limitations
The potential is finite and bounded; hard constraints with log-potential −∞ are outside this claim. Lean checks only finiteness of the variational value for bounded continuous potentials, not the free-energy convergence or the bounded-Borel extension.
Technical verification
OpenAI reports a Lean check of a narrower theorem, case, or component; the selected claim extends beyond that scope.
Formal checking
The pinned OpenAI Lean scope note verifies only this narrower statement, not the full selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For nonnegative pattern density and bounded continuous log-potential, the selected overlap-path variational infimum is a finite real number.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and precise Lean-scope or conditional-input review for non-notifying local inclusion.
Read this published revision