# Pure infiniteness and absorption contract

Family 303: Weak pure infiniteness and Cuntz-algebra absorption. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize equivalence of ordinary and strong pure infiniteness and restricted absorption consequences.

## Applicability and commercial boundary

Exact fixed-amplification conditions and separable nuclear assumptions must be preserved; no finite numerical detector is supplied.

## 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

Map each implication and the operator-algebra class.

## 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).

[Weak pure infiniteness and O-infinity absorption](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf).