# Rigid lattice bimodule classification reference

Family 286: Rigidity and arithmetic of lattice von Neumann algebras. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize finite-index bimodules and stable equivalence for the specified rigid lattice von Neumann algebras.

## Applicability and commercial boundary

ICC, property-T, commensurability, local-field, cocycle and amplification hypotheses matter; classification is not an implemented finite solver.

## 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 representatives and computable invariants.

## 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).

[Arithmeticity of twisted finite correspondences for lattices over local fields](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf).