# Case 07: Restricted-host accepted-swap mixing

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 structurally restricted host reaches the source uniform degree-fiber mixing guarantee after counting accepted swaps only.

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/131.md](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/131.md), SHA-256 `95890a0433c375da400f600f581f1eb352416bc25f720c3483767022ce3fba4c`.
- [preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/main.pdf](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/main.pdf), SHA-256 `e70eab92c1315e6706eea3613e9826871e009d1ef8de31f82d5750d026240af3`.

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.