Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 175-01. Graph Decompositions at the Integral Expectation Threshold
Manuscript map · lines 5625–5634
OpenAI@2026-10-07#rem:oai-p-175-01
Authors: OpenAI. Family 175.
Title: Graph Decompositions at the Integral Expectation Threshold.
Abstract: We prove the graph-decomposition conjecture of Ascoli, He, Park, and Talagrand. Every graph admits a partition into a universally bounded number of fixed edge pieces, each having ordinary containment threshold at most a universal constant times the original graph's integral expectation threshold. The partition is chosen before sampling the random host, and the separate embeddings of the pieces need not agree on shared vertices.
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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