What was already known
Each fixed dimension admits polynomial-time tuple refinement. Earlier work showed coNP-hardness when dimension varies and posed the EXPTIME question.
AI involvement
OpenAI is credited as author of the model-produced reduction and proof. No claim-specific human check or explanation of the construction is documented.
OpenAI is credited as author of the model-produced proof and the repository documents the internal model's central research role.
Importance
The result answers the stated complexity question and extends hardness to subcubic graph pairs.
Limitations
The claim concerns joint-update equivalence under the stated encoding and reductions; graph identification and the published parity-lift construction are different results.
Technical verification
OpenAI’s formalization catalogue maps the general and connected-subcubic EXPTIME-completeness statements, including binary dimension encoding and adjacency-matrix inputs, to its Lean comparator.
Formal checking
Lean proof of variable-dimension equivalence complexity under the stated graph and input encodings
- Checker
- OpenAI Lean 4 library and comparator
- Scope
- Joint-update variable-dimension Weisfeiler–Leman equivalence is EXPTIME-complete on general and connected subcubic graph pairs under the stated input encoding and reductions
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The model-produced manuscript explains the reduction, but no human account establishing understanding of its central construction was located; Few is the evidence default, not a report of human incomprehension.
Correction and publication history
The result answers the stated complexity question and extends hardness to subcubic graph pairs.
Read this published revision