# C-star similarity hypothesis contract

Family 288: Kadison's similarity conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track when a bounded complex-linear unital homomorphism is similar to a star homomorphism.

## Applicability and commercial boundary

The bounded invertible similarity operator need not be well conditioned, small or efficiently computable.

## 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

Extract quantitative similarity bounds and a finite restricted 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).

[Kadison's similarity theorem through uniform derivation estimates](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026/paper.pdf).