What was already known
Unrestricted exponential lower bounds were known for linear extensions, and exponential semidefinite bounds were known under coordinate symmetry. Neither excludes an unrestricted small exact semidefinite lift.
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
Rules out subexponential exact semidefinite formulations of the perfect-matching polytope without a symmetry assumption.
Limitations
The manuscript derives this from an exponential PSD-rank bound for positively shifted odd-cut slack matrices. The linked Lean scope establishes only a superpolynomial lower bound for exact affine semidefinite lifts; it does not certify the exponential rate or the positively shifted matrix theorem.
Technical verification
OpenAI reports a Lean check of a narrower theorem, case, or component; the selected claim extends beyond that scope.
Formal checking
The pinned OpenAI Lean scope note verifies only this narrower statement, not the full selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every fixed C>0, exact affine semidefinite lifts of the perfect-matching polytope eventually require matrix size greater than n^C.
- 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 precise partial or mismatched Lean-scope review for non-notifying local inclusion.
Read this published revision