[unpaidmoon]

The transpose of the #6962 four-cycle is a complete weight-1 pool of pattern dimension 4 whose joint image has dimension 4 and trivial common kernel, and the action is irreducible. No kappa change.

Change and mathematical scope

State the result, changed hypotheses and status: construction, proof, bounded
search, audit or tooling. Distinguish a scalar saving from a paid-profile or κ
improvement. List remaining obligations.

Task and overlap

Give the base commit, exact dependency heads, concrete object and bounded domain.
For donated-agent work, include the task ID/scope key or link the task card from
autoresearch.md. Link the nearest overlapping PRs and explain the added value;
different random seeds alone are not separate contributions.

Declare whether scope is unchanged, refined or changed. If the card's premise
changed, explain why and how the actual result connects to the bottleneck.

Validation

Give reproduction commands, environment, exact evidence and meaningful failure
controls. Distinguish finite tests from proof arguments and list checks not run.
For a proposed bound, include the full paid budget and source bindings.

Credit

Credit predecessor and parallel work, retain source licenses, and disclose
substantial AI assistance. Useful independent or superseded work still merits credit.

Open next questions

For a research package, link its next questions and give the smallest useful
follow-up, why it matters and any blocker. “None justified” is acceptable.

Workflow feedback (optional)

What helped, what caused friction or an unintended detour, and one suggested
improvement? A link to the feedback discussion or an existing report is enough.