# Compressed strong paving scope audit

Family 300: Approximation and quadratic strong-operator paving. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Investigate the quadratic block-count bound for strong-operator paving after compression near the identity.

## Applicability and commercial boundary

Compressed strong paving is distinct from uncompressed operator-norm paving. A block-count bound does not imply an efficient finite algorithm.

## 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 constants, topology and finite constructive examples.

## 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).

[Approximation Paving over Arbitrary Maximal Abelian Subalgebras](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf).