Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 133-03. Unconditional time lower bounds for Weisfeiler–Leman equivalence
Manuscript map · lines 4985–4994
OpenAI@2026-10-07#rem:oai-p-133-03
Authors: OpenAI. Family 133.
Title: Unconditional time lower bounds for Weisfeiler–Leman equivalence.
Abstract: For every sufficiently large fixed k, deciding whether two n-vertex graphs are k-Weisfeiler–Leman equivalent requires $n{}{{}Omega(k)}$ deterministic sequential time in the worst case. The bound holds at every sufficiently large graph order, even for simple connected uncolored graphs of diameter at most two, without a complexity assumption. Inputs are explicit adjacency matrices; the models are multitape Turing machines and sequential logarithmic-word RAMs with fixed polynomial-bit-time instructions. Both joint and separate replacement conventions are covered.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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