Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 302-01. Filtered products and boundary-preserving compression in complex cobordism
Manuscript map · lines 8375–8384
OpenAI@2026-10-07#rem:oai-p-302-01
Authors: OpenAI. Family 302.
Title: Filtered products and boundary-preserving compression in complex cobordism.
Abstract: We prove that, in sufficiently large smash powers, an $MU$-null restriction to a finite pointed subcomplex becomes stably null on the entire union of products with a fixed positive proportion of restricted factors. This coherent vanishing theorem yields boundary-preserving compression of cube-valued maps on every compact metrizable input space. When the torus slot bundle embeds continuously into a trivial bundle of rank less than twice the source rank, the compression places a positive proportion of slots on their boundaries in arbitrarily large powers and fixes every original boundary slot exactly. An example at equality shows that the strict rank inequality cannot be removed.
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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