What was already known
Blass, Gurevich and Shelah conjectured that choiceless polynomial time with counting does not capture all polynomial-time queries on unordered finite structures. Earlier separations did not establish this for the full counting formalism.
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
Resolves the noncapture conjecture for the full choiceless counting formalism.
Limitations
The query is total on finite inputs and uses a fixed vocabulary. The separate witnessed-symmetric-choice extension is a different result in this family.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers an explicit polynomial-time isomorphism-invariant query on all finite structures that is outside the stated full hereditarily finite-set counting language.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- An explicit isomorphism-invariant query on all finite structures in one fixed vocabulary of eight relations is decidable in deterministic polynomial time but is not definable in choiceless polynomial time with counting.
- 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