Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 318-02. The height-three chromatic overlap: an explicit filtration and its attachments
Manuscript map · lines 8595–8604
OpenAI@2026-10-07#rem:oai-p-318-02
Authors: OpenAI. Family 318.
Title: The height-three chromatic overlap: an explicit filtration and its attachments.
Abstract: For every prime p ≥ 5, we construct an explicit eight-stage filtration of $L_2L_{K(3)}{}mathbb S_p{}{}wedge$ by the local-sphere layers in the height-three chromatic-splitting pattern. The map from its first stage to the overlap is the canonical unit, and two signed fracture formulas identify all attachments for the chosen local maps and compatibility homotopy. A companion canonical-map theorem further implies that the first height-one attachment is nonzero.
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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