Discoveries / geometry-topology

Source authenticated

The coarse Novikov conjecture for bounded-geometry spaces: is coarse assembly rationally injective?

Claims a uniformly discrete bounded-geometry space $X$ , a coarse disjoint union of finite connected graphs of uniformly bounded degree, with an infinite-order class $\alpha\in KX_1(X)$ whose image under ordinary coarse assembly into $K_1$ of the reduced locally compact Roe algebra vanishes, so $\mu_X$ fails to be injective integrally and rationally. The companion (5 October 2026) claims the same kind of class is killed already by maximal coarse assembly, which implies the reduced statement. Earlier kernel examples (Yu; Dranishnikov-Ferry-Weinberger) lacked bounded geometry or died under coarsening. It does NOT give a counterexample to the Novikov conjecture or to Baum-Connes for groups, nor a space with property A or coarsely embeddable into Hilbert space.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. 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: The coarse Novikov conjecture for bounded-geometry spaces: is coarse assembly rationally injective? · Coarse Novikov conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The coarse Novikov conjecture for bounded-geometry spaces: is coarse assembly rationally injective?

specialist registry · passed

No independent mathematician has checked this yet. Theorem 1.1 of both manuscripts was read against the coarse Novikov conjecture. A Lean challenge lean/ComparatorChallenges/CoarseAssembly.json (solution module OAI.Topology.CoarseAssembly, present at the pinned commit) exists but is not in the formalization catalogue; found through lean/docs/307.md. Its statement was read here and does not settle the tier: the 6600-line challenge defines its own graphs, Roe algebra, K-theory and an assembly map from a bespoke analytic index family, and that family (separatedIndexFamily) is defined to be the zero map whenever its scale-wise indices are not compatible. In that case the asserted vanishing $\mu(\alpha)=0$ and non-injectivity hold trivially, so the formal statement need not express the headline. Under the strict tier rule the entry stays Unreviewed. Not rebuilt here.