Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 133-01. Parity lifts and bounded-treewidth witnesses for Weisfeiler–Leman equivalence
Manuscript map · lines 4965–4974
OpenAI@2026-10-07#rem:oai-p-133-01
Authors: OpenAI. Family 133.
Title: Parity lifts and bounded-treewidth witnesses for Weisfeiler–Leman equivalence.
Abstract: For k ≥ 4, we construct two uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when a prescribed finite-domain choice system has no compatible choice. The system has $k+1$ domains for joint refinement and k for separate-coordinate refinement. A successful choice is detected after two joint rounds or one separate round. Applied to sparse satisfiability, the reduction gives fixed-dimension $n{}{{}Omega(k)}$ time exclusions under positive-rate ETH, even for deciding equality of these early histograms.
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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