What was already known
Earlier parity constructions connected graph equivalence to linear constraints; the manuscript extends that approach to arbitrary finite-domain pair-label compatibility with specified early-round detection.
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
Gives a direct reduction from simultaneous finite choices to bounded-dimension graph refinement.
Limitations
For joint refinement the system has k+1 domains, and for separate refinement k domains. The Lean scope checks this parity-lift construction; the manuscript’s ETH-based running-time exclusions are a separate consequence outside the selected check.
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
- For each k≥4, an explicit construction maps a finite compatible-choice system to two equal-size simple uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when the system has no successful choice; a successful choice is detected after two joint-refinement rounds or one separate-refinement round.
- 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