# Continuous symmetry classification contract

Family 304: The Hilbert–Smith conjecture in every dimension. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record the Lie-group consequence for a faithful continuous action on a finite-dimensional connected topological manifold.

## Applicability and commercial boundary

Local compactness, second countability and faithfulness matter. A finite observation of transformations is not a proof of these assumptions.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Inspect effective recognition or an explicit action example.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The Hilbert–Smith conjecture in every finite dimension](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026/paper.pdf).