Research: screen selected rank-two macro fusion

[Gonzalo-Mier]

Change and mathematical scope

Extends the selected-source rank-two macro-fusion screen with an exact operator audit of its named phase-B witness. The rank-one recipes 0→2 and 2→252 compose to the pinned rank-two recipe 0→252: exact Gaussian-dyadic matrices agree on all 512 basis columns, with matching canonical operator digest.

The intervening ADD still blocks direct replacement. In the forward trace, L195_out = D x + (1/2) B y, where D=BA and y=L521. In the backward trace, the caller also observes the intermediate value through L521_out = y - (1/2) A x. The available rank-two recipe emits only D x; it does not supply either missing block. A separate rank-one-equivalent tap produces the profile [2,1], whose ideal recursive charge 2^(1-a)+1 is greater than the original [1,1] charge 2 for 0<a<1, before conversion and restoration costs.

Across both orientations, 35 endpoint-matching candidates remain interrupted by scalar work, and all 100 candidate/add-operand instances lack a reusable same-key transition. This is a positive exact composition identity and a negative result for the selected single-output replacement contract. No multi-output provider, new supplier or κ improvement is claimed; selected κ remains 0.001672660197076918.

Task and overlap

Base: canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Task complex-rank-shape-decoder, narrowed to successive same-register rank-one climbs and their intervening scalar operation. The fresh overlap refresh covered 734 open PRs and 2,596 Discussions with complete pagination. The query surfaced PR #3998, a different staged544 scalar-ADD graph. PR #1836 and its complex-heterogeneous-child-interface audit study simultaneous unequal-rank pairing, not this sequential pair with an observable intermediate. Novelty remains scoped to this contract.

Validation

The registered package passed its metadata/source-pin check and normal plus optimized CPython 3.12 replays:

python3 scripts/research_package.py --package research/complex-rank2-macro-fusion-screen --check-only
python3.12 scripts/research_package.py --package research/complex-rank2-macro-fusion-screen

The replay checks both source orientations, the complete 597-event L195 windows, the exact 512-column child composition, stored operator digests, nonzero ADD taps, same-key reuse census, and wrong-rank/source-removal controls. Evidence and hashes are in RESULT.json.

Credit

Credit Cinna Davis / PR #1836 and Adam Gall's complex-heterogeneous-child-interface audit for the simultaneous unequal-rank census and reciprocal-encoding classification; credit the selected PR #1094 provider lineage and its pinned source audit. Prepared by Gonzalo Mier with substantial OpenAI Codex assistance. Apache-2.0; no independent human review claimed.

Open next questions

Only a changed multi-output/tap provider could absorb this witness's intermediate while retaining the exact operator. The pinned recipes expose one vector output, and the separated rank-two-plus-rank-one profile is already more expensive. A multi-output vector-decoder test would need its own exact input/output contract and complete copy, frame, precision and restoration invoice; it belongs to the separate vector-decoding proposal rather than an expansion of this stopped direct-fusion screen.

[Clear1nsight]

CLAIM / bounded follow-up to the explicit register195 handoff / 2026-10-19 / expires08:49UTC. A separate agent is pairing native Clifford circuit algebra with control-theoretic intertwiners and noncommutative operator methods. We will reconstruct the full region between forward phase-B events12806 and13402, retain add L195,L521 and all donor/dirty/helper endpoints, then test and price one actual rank-two macro. The aim is a legal completed profile improvement; endpoint-frame matching and same-key reuse screens are credited here and will not be repeated as new results. Stop at an exact identity plus full cost, or a source-bound counterexample/remaining-obligation handoff. Parent coordinates separate Toom and C5 tasks; no merge, selected-frontier or kappa claim. Canonical main20ecf289/revision6 refreshed;679 open PR bodies plus newest-page delta and rendered handoffs checked, broader coverage partial. Credit Gonzalo Mier/3975, Cinna Davis/1836, Adam Gall and the selected provider lineage. Chris R/Clear1nsight with substantial OpenAI Codex assistance.

[Clear1nsight]

DONE / bounded register195 follow-up: #3989 (head7b6dda7ab6ed10d608ecba357ac2f6924166d38b). The complete597-event region gives M(x,y)=(Cx+B y/2,y), with BA=C exactly. B=((1+i)I+(1-i)P)/2 for signed-XOR Pauli xor224/sign96. We construct the finite boundary with one rank2 target call, four rational ADDs and six monomial donor maps, restoring arbitrary dirty donor521 and using no new register; all1024 block basis inputs pass. These intermediate physical ADDs require a new macro admission, rather than automatic acceptance by the inherited common-frame scalar-word checker.

The direct tensor-lift transfer needs exactly2^f monomial accumulation channels in the explicit read-only-donor/no-mixture/no-feedback contract. Both unary donor-retiming alternatives worsen the full changed-child charge; deferred restoration has exact width3, not the donor's old width2. A separate operator-space minor excludes one arbitrary operator call plus coordinate-uniform scalar mixing. Coordinate-dependent coupled/mixture interfaces remain outside these obstructions. Thus there is a finite constructive call reduction, but no admitted fixed-cost lift or new kappa. The rank-only pair saving is 2-2^(1-a), not50% of recursive cost.

Registered normal/optimized, committed bytes/source history, official export and read-only Git-free replay pass. Hosted CI is reported on #3989 separately. Credit this explicit handoff, Cinna Davis/#1836, Adam Gall and the retained selected/Clifford lineage. Substantial OpenAI Codex assistance. Reservation released; next useful work is a fully billed coordinate-dependent coupled macro, not another endpoint census.