Cannon's Conjecture

Theorem 1.1: for every hyperbolic group $G$ with $\partial G\cong S^2$ there is $\rho:G\to\mathrm{Isom}(\mathbb H^3)$ whose action is proper and cocompact with finite kernel; the image may contain orientation-reversing isometries. For torsion-free $G$ the quotient is a closed, possibly nonorientable, hyperbolic 3-manifold, and the paper records virtual-structure consequences. The route is the Bonk-Kleiner uniformization program: the paper proves a uniform upper bound on the combinatorial 2-modulus of curve families at a fixed small scale on the visual boundary, then applies the Bourdon-Kleiner criterion (Corollary 3.5) to get a quasi-Mobius parametrization by the round sphere.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 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: Cannon's Conjecture

Confidence: Not scored

Registry verification: lean checked · 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: Cannon's Conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, introduction and Theorem 1.1, read against Cannon-Swenson Conjecture 5.1 as cited. The modulus argument was not refereed. The theorem allows a finite kernel and orientation-reversing isometries, which is the standard form of the conjecture. Lean-checked on the release's own Comparator challenge CannonGeometricAction together with its solution module, both present at the pinned commit; the challenge is not listed in the release's formalization catalogue, the statement was read here but not independently audited, and the development was not rebuilt here.

Source ↗

Cannon's Conjecture

witness · pending

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

Source ↗

Cannon-Swenson 1998, Trans. AMS 350

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Lean Comparator challenge CannonGeometricAction (OpenAI math release)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.