feat(research): share the rank-seven restore covector

[petalas]

Summary

R2 shares the current-register covector X40 - 2 X54 across two separated restore consumers on PR2979's words, then restores both dirty sources. It composes with Jeremy Kothe's R1 from #3015.

 R1 local profile
- {1:2443, 2:707, 3:232, 4:108, 5:18, 8:8}
+ {1:2441, 2:708, 3:232, 4:108, 5:18, 8:8}

The per-call delta is H2 - 2H1 < 0 for every positive saving. The literal T74 allocation, all ordered widths, 91 private buffers and scalar gate counts are unchanged.

Proof, sources, full invoice and reproduction. Canonical investigation and handoff.

Evidence

• Before: feat(research): release the T740 R1 cap composition #3030's released T740+R1 nomination is 0.001729152756004330934535 - 10^-46 - 10^-70.
  After: a fresh complete T74 source/native/admission/modern-outer release certifies 0.001729267980311944693216 - 10^-46 - 10^-70. Exact gain 115224307613758681/10^24.
• Separate 704-column rational restore equality and four-register set-span census; both providers pass 632-input forward/dual audits. Sixteen rejecting word/contract controls and ten behavioral groups pass.
• Fresh retained bootstrap and both fresh native providers; thirteen stages total 1,272.70 seconds locally. The emitted invoice charges 66,813 physical families, all 666 invocation/bridge sweeps, and prefix 1,475 within payload 2,048.
• Registered Python 3.12 replay, optimized replay, Python 3.13 finite replay, ten receipt/invoice mutants, strict lint, compilation and all 53 committed package/input-byte comparisons pass. Hosted CI is separate.

python3.12 -B scripts/research_package.py --package research/rank7-shared-restore-fanin

Credit Jeremy Kothe for R1 and the literal edit tooling, Marius-Paul Dumitrean for PR2979, and the retained geometry/native/owner lineage. Original notices remain. New R2 and this composition are by Nick Petalas.

Merge Danger

Door: two-way

Blast Radius: isolated

Only a new research package and its opt-in replay are added. Frozen predecessors and the selected frontier are unchanged. This is an author-checked conditional finite candidate, not scientific adoption or a complete multiplication theorem. Inherited all-size/compiler, physical, precision/tape, caller, analytic and universal block-energy hypotheses remain. Independent review/replay and a separately bound T740+R2 composition are open next questions.