What was already known
Earlier hardness results used a finite orbital basis or restricted molecular input models. Those reductions did not establish hardness of the full antisymmetric continuum energy with the stated binary-charge encoding.
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
Establishes quantum complexity hardness directly for a continuum Coulomb Hamiltonian with unrestricted spin sectors.
Limitations
The charge values and inverse nuclear separations can be exponentially large despite polynomial descriptions. The claim is hardness, not QMA membership or hardness for unit charges.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers a deterministic polynomial-time many-one QMA-hardness reduction for binary-encoded charges, full continuum antisymmetric states and all spin sectors.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Approximating the electronic Coulomb spectral infimum in three-dimensional continuum space is QMA-hard when positive integer nuclear charges use binary encoding, nuclei have distinct rational positions and electron count is unary; a deterministic polynomial-time reduction produces a promise gap of at least one.
- 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