Mathematical FrontierNetworkSubmit movement

Discoveries / geometry-topology

Source authenticated

The Hilbert-Smith Conjecture

For every n≥1n\ge 1, every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected Hausdorff second-countable topological nn-manifold without boundary is a Lie group. The core theorem is that every continuous Zp\mathbb{Z}_p-action on such a manifold has nonzero kernel, by a contradiction between pkp^k equal integral classes summing to a fixed class and a fixed denominator bound in a Witt-group lattice. Noncompact, nonorientable and nontriangulable manifolds and arbitrary stabilizers are allowed. Manifolds with boundary are not treated.

Exact FrontierDelta

Prior state unknown→proved

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 Hilbert-Smith Conjecture · Hilbert-Smith 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

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

VibeMathed record: The Hilbert-Smith Conjecture evidence for this event

For every n≥1n\ge 1, every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected Hausdorff second-countable topological nn-manifold without boundary is a Lie group. The core theorem is that every continuous Zp\mathbb{Z}_p-action on such a manifold has nonzero kernel, by a contradiction between pkp^k equal integral classes summing to a fixed class and a fixed denominator bound in a Witt-group lattice. Noncompact, nonorientable and nontriangulable manifolds and arbitrary stabilizers are allowed. Manifolds with boundary are not treated. parent of this event

The Hilbert-Smith Conjecture parent of this event

The Hilbert-Smith Conjecture evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verifyOpen canonical problemExplore evidence graph