# Case 06: Numerical polynomial-time Artin membership

Self-authored synthetic review scenario, not a published software claim or customer assertion. The source material is public and pinned to `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`.

## Proposed claim

A numerical coefficient backend is independently verified to implement polynomial-time membership in every finite-rank Artin parabolic.

Review the [declared model and statuses](input.json) against the source. Cases 09/10 deliberately supply synthetic statuses to test documentary completeness. Those statuses are not authenticated evidence or proven hypotheses. Other cases explicitly leave operational obligations unknown.

## Source pointers

- [lean/docs/254.md](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/254.md), SHA-256 `327dfb32694d5072c4a47aff41da516a7cbe663634285577f344beb98d94d4e2`.
- [preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/paper.pdf](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Parabolic-intersections-in-Artin-groups-September-23-2026/paper.pdf), SHA-256 `4cd7fa316371447c2cb8a99d36bf9f48934c2366550609917210574e3f4f7e2e`.

Pointers identify exact files, not a new complete-file reading, theorem proof or selected-run certificate. Determine the statement, hypotheses, formal coverage and missing model/implementation bridges from the source itself.

## Review fields

Record preparation seconds, material gaps with exact evidence locations, unsure items, false alarms after adjudication and correction seconds in the [blank result template](../review-results-template.json). Do not open the report/key during the source-only arm. No expert has completed either arm.