Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 318-04. Failure of finite assembly for a chromatic overlap at the prime three
Manuscript map · lines 8615–8624
OpenAI@2026-10-07#rem:oai-p-318-04
Authors: OpenAI. Family 318.
Title: Failure of finite assembly for a chromatic overlap at the prime three.
Abstract: At the prime three and height three, the chromatic overlap cannot be constructed from the rational, height-one, and height-two local spheres by finitely many sums, shifts, cofibers, and retracts in the category of $E(2)$-local modules over the derived 3-complete sphere. This gives a negative answer to the ordinary finite-assembly question for chromatic overlaps.
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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