Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 318-05. Counterexamples to weak chromatic splitting: sphere kernels and descent exponents
Manuscript map · lines 8625–8634
OpenAI@2026-10-07#rem:oai-p-318-05
Authors: OpenAI. Family 318.
Title: Counterexamples to weak chromatic splitting: sphere kernels and descent exponents.
Abstract: For the derived p-completion of the sphere, the canonical weak chromatic splitting map has no homotopy retraction at height p for every prime p ≥ 5, and at height $p+1$ for every prime p ≥ 7. The classical sphere product ${}beta_1{}{(p-1){}2}$ gives a nonzero kernel class in both ranges.
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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