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Math-2825 · mathematics · Analysis

Filtered smash products of cobordism-null restrictions

Status OpenLLM status Open unverified

Statement

Definitions and mathematical statement

Statement recorded in the supplied source.
Given a finite pointed CW pair $G\subseteq E$ and a based map $v:E\to S^d$ whose stable restriction to G becomes null after the unit $S\to MU$, does $v^{\wedge \ell }$ become stably null on the union of smash products with at least $ceil(\ell /2)$ factors restricted to G, for every sufficiently large $\ell $?

Short English statement

Given a finite pointed CW pair $G\subseteq E$ and a based map $v:E\to S^d$ whose stable restriction to G becomes null after the unit $S\to MU$, does $v^{\wedge \ell }$ become stably null on the union of smash products with at least $ceil(\ell /2)$ factors restricted to G, for every sufficiently large $\ell $?

Sources

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Math-2825-A1 · Literature report · LLM-generated · unknown ·

OpenAI claim summary for Math-2825

Manuscript 1 (family 302, 2026-09-25): The problem selects the mathematical statement summarized here, including its stated hypotheses and parameter range. The cited theorem gives a claimed proof of that assertion in full.

Filtered smash products of cobordism-null restrictions

OpenAI's claim

Cobordism-null restrictions are claimed to vanish coherently on large constrained smash-product unions, yielding boundary-preserving cube compression under a torus-bundle embedding of rank strictly below twice the source rank. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
Let $G\subset E$ be a finite pointed CW pair, $d\ge0$, and $v:E\to S^d$ based. Assume the restriction of its stable class to $G$ becomes null under the complex-cobordism unit: \[ \Sigma^\infty G\to\Sigma^\infty E\xrightarrow{\Sigma^\infty v}\Sigma^d\mathbb S\to\Sigma^dMU\simeq0. \] For $\ell\ge1$ let $U_\ell\subset E^{\wedge\ell}$ be the union of subcomplexes with at least $\lceil\ell/2\rceil$ factors in $G$. OpenAI claims $v^{\wedge\ell}|_{U_\ell}:U_\ell\to S^{d\ell}$ is stably null for every sufficiently large $\ell$. The conclusion is about stable nullhomotopy on the specified family of product subcomplexes.

Outline of the argument

Manuscript 1 (family 302, 2026-09-25): Product filtrations grow linearly while a uniform connective nilpotence cutoff grows sublinearly, forcing stable vanishing across the entire constrained union. Compatible local duality turns the vanishing into avoidance, and radial normalization restores old boundary slots. Padding and a coordinate-preserving polyhedral model remove input-dimension restrictions while retaining a positive boundary fraction.

Formal verification

Family 302 has no Lean scope page in this snapshot; no formalization of these manuscript results is listed.

This site has not executed the Lean files or checked their dependencies. These descriptions report the scope of the linked declarations, rather than a new verification of the proofs.

Status caveat

OpenAI attributes these results to an internal model. Its release notice cautions that results lacking full formalization can contain mistakes. This site has not independently assessed the proofs; a solved label records the scope of the reported claim.

Sources

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