What was already known
Simon asked for a continuum temperature singularity with suitable stable pair interactions. Earlier constructions used multiple species, many-body terms, modified Kac terms or a single coexistence density.
AI involvement
Both September 2026 manuscripts credit OpenAI, and the release says its internal model produced the collection. The bounded potential, multiscale attraction construction and common-temperature density interval are model-output claims. Result-specific human input is undisclosed.
OpenAI is author of the model-produced bounded-core construction and its distinct companion; no specific human-origin account displaces that attribution.
Importance
Gives a bounded-core existence construction with one critical temperature over an open density interval.
Limitations
A separate divergent-core manuscript has a different potential. These results do not concern Lennard-Jones or identify conventional fluid phases.
Technical verification
The release formalization catalogue lists both manuscripts; the family 228 note maps the bounded continuous potential and open density interval to a Lean solution theorem. This is source-reported machine formalization of the assessed bounded-core statement, not a locally reproduced build or a check of physical phase interpretation.
Formal checking
Lean theorem RadialTransition.densityInterval and related family 228 formalization, mapped by the scope note
- Checker
- Lean proof checker, as reported by OpenAI's formalization catalogue
- Scope
- Stable bounded continuous radial potential with algebraic tail and a common inverse-temperature derivative jump on an open density interval
- 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. The model-authored articles describe the multiscale pressure-support mechanism, but no named human explains it or reports understanding; this is a missing-evidence default.
Correction and publication history
Gives a bounded-core existence construction with one critical temperature over an open density interval.
Read this published revision