What was already known
Györgyi and Reimann predicted the continuous replica-symmetry-breaking spherical formula in 2000. The prediction did not prove pressure convergence.
AI involvement
OpenAI credits an internal model with producing the mathematical results in this collection. Humans chose and organized problems; no named human explanation of this theorem is documented.
The collection's model-production account and OpenAI authorship support model-led mathematical work, without a per-result autonomy account.
Importance
The result gives a rigorous finite-temperature formula for the spherical model across the stated class of potentials.
Limitations
The result concerns the spherical model; the Ising model and zero-temperature jamming are separate. Identification with the predicted Györgyi–Reimann functional rests on the repository description rather than a direct comparison with the manuscript text.
Technical verification
The Lean scope identifies the complete bounded-continuous spherical pressure formula, including finiteness and convergence in expectation and probability. The comparator is a target statement; the linked development supplies its proof.
Formal checking
Lean proof of the spherical pressure theorem under the stated hypotheses
- Checker
- OpenAI Lean development and Lean type checker
- Scope
- Spherical-perceptron variational pressure formula for positive density and temperature and bounded continuous potential, with expectation and probability convergence
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human account explaining the central variational mechanism was located; Few is the evidence default, not a finding that people cannot understand it.
Correction and publication history
The result gives a rigorous finite-temperature formula for the spherical model across the stated class of potentials.
Read this published revision