What was already known
Earlier continuum phase-transition constructions used a two-species model or different hard-core and thermodynamic settings. The manuscript addresses a single radial pair potential with a temperature derivative singularity over an interval of fixed densities.
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
Constructs a rigorous temperature-driven singularity for a stable three-dimensional continuum pair potential.
Limitations
The selected potential has an o(r⁻³) tail but no proved fixed r⁻³⁻ε power margin; the manuscript says it does not settle historical formulations requiring that stronger decay.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- One stable radial pair potential in three dimensions with a divergent repulsive core and integrable o(r⁻³) tail has canonical free energy at all positive temperatures and densities, with a strict finite jump in its inverse-temperature derivative at one common positive temperature over a nonempty open interval of densities.
- 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 scoped checking review for non-notifying local inclusion.
Read this published revision