Rule out four-read retiming after removing helper 584

[RossRichardson]

Summary

• Removing helper 584 preserves the exact circuit algebra, but rearranging four shared-source reads cannot satisfy the required frame constraints.
• The proof covers all 1,002 contact-order classes on each of two pinned research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (κ = 0.0017297760894) #3133 circuits. All 2,004 classes have input-to-output obstruction paths that avoid native boundaries. Changing frames or phases at existing native slots, or changing helper entrance/terminal frames, cannot repair this family.
• Adds only research/direct584-commuting-retiming-cover/: a written completeness proof, fixed certificates, source pins, a standalone exact interpreter and the registered replay hook. This closes the gap between checking a few placements and covering the whole stated family.

Scope and limits

The result fixes the two dimension-nine source circuits, moves only four reads by adjacent commuting swaps inside B, and preserves the remaining scalar order and native-slot locations. Changed scalar consumer networks, added/moved native slots and changed input/output contracts remain open.

No cheaper supplier, improved κ or selected-frontier change is established. The original κ > 0.00173 research target remains unachieved. This is a finite obstruction with executable evidence and a written coverage argument; no formal-kernel proof or general helper-removal barrier is claimed.

Test plan

• python3.12 -B research/direct584-commuting-retiming-cover/verify.py — fresh replay passed at e3dc9c1660bfec0501dd7522f44a21746f9b89e2.
• python3.12 scripts/research_package.py --package research/direct584-commuting-retiming-cover — local registered replay and hosted CI passed.
• Exact predecessor source pins and committed publication bytes checked; Git-free optimized replay passed.
• Independent maintainer mathematical review.

Replay checks all 2,004 paths and 20 rejection controls. Full arbitrary-dirty forward/dual algebra checks cover the original placement and two extreme representatives per circuit: 12 checks on 631 independent inputs and 90 private buffers. A written commutation argument covers the remaining placements; full algebra replay of all 2,004 classes is not claimed.

Supplementary AI review found no material gap within this scope. Its separate coverage-review script remains local and is not a public replay input or independent human review.

Sources and credit

Source: #3133 at 51eb9c4ee9e4722010d308aa3309e039d3940cc2; base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Credit dcharb78, Marius-Paul Dumitrean (#2979), Jeremy Kothe (#3015) and the source's retained contributor lineage.

Prepared by Ross Richardson with substantial OpenAI Codex assistance. Canonical finding and open next question.