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Existence of bounded-degree F2 coboundary expanders in every dimension

Theorem 1.1: for every $d\ge3$ there are $D$ , $\varepsilon>0$ and finite connected pure $d$ -dimensional complexes $X_m$ with $|X_m(0)|\to\infty$ , every vertex in at most $D$ top faces, and $\|\delta_if\|\ge\varepsilon\,\mathrm{dist}(f,B^i)$ for all $i<d$ . The complexes are $d$ -skeleta of congruence quotients modulo $t^m$ of a coset complex for the Iwahori-type subgroup of $\mathrm{SL}_{2d+1}(k[t])$ over a large odd prime field; cohomology vanishing comes from an affine twin building, and quantitative expansion from Oppenheim-Valentiner-Branth. Constants depend on $d$ and are not explicit; only $\mathbb{F}_2$ coefficients are treated.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Existence of bounded-degree F2 coboundary expanders in every dimension · Bounded-degree coboundary expanders

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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VibeMathed record: Existence of bounded-degree F2 coboundary expanders in every dimension

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, introduction and Theorem 1.1 of the TeX source, read against the problem as cited from Gromov (2010) and Chapman-Lubotzky (2025); the proof was not refereed. Lean: the Comparator challenge CoboundaryExpanders (OAI.CoboundaryExpanders.main, solution module OAI/Combinatorics/Coboundary/Main.lean) is not in the release's formalization catalogue, but its JSON and solution file exist at the pinned commit. Its statement was read here: for every d >= 3 there are D, eps > 0 and a sequence of finite pure connected d-dimensional complexes with vertex counts tending to infinity, at most D top faces at each vertex, and eps times the weighted distance to coboundaries at most the weighted norm of the coboundary in every degree i < d. This is the headline claim; the graph and two-dimensional cases are prior work. Not rebuilt here. The construction uses the cosystolic expansion theorem of Oppenheim and Valentiner-Branth as an input.

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Lean: OAI/Combinatorics/Coboundary/Main.lean (CoboundaryExpanders.main)

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lean-proof link supplied by the VibeMathed registry.

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Chapman, Lubotzky, Stability of homomorphisms, coverings and cocycles II (Adv. Math. 2025)

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problem-record link supplied by the VibeMathed registry.

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Existence of bounded-degree F2 coboundary expanders in every dimension

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Artifacts and verifiers

Lean: OAI/Combinatorics/Coboundary/Main.lean (CoboundaryExpanders.main)

lean artifact · pending

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This event attributed to Unreleased internal OpenAI model

Existence of bounded-degree F2 coboundary expanders in every dimension parent of this event

Chapman, Lubotzky, Stability of homomorphisms, coverings and cocycles II (Adv. Math. 2025) evidence for this event

Existence of bounded-degree F2 coboundary expanders in every dimension evidence for this event

VibeMathed record: Existence of bounded-degree F2 coboundary expanders in every dimension evidence for this event

Lean: OAI/Combinatorics/Coboundary/Main.lean (CoboundaryExpanders.main) evidence for this event

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