Research: share rank-eight output delta across dirty accumulators

[1337isnot1337]

Result

Adds a bounded recursive-interface construction package for paired dirty scalar outputs. If a rank-eight additive child computes f(x,y)=sum(i=0..7) x_i*y_i, then repeating

NEG(D1); ADD(D2,D1); NEG(D1); child_plus(D1); ADD(D2,D1)

twice maps arbitrary (D1,D2) to (D1+2f,D2+2f). It replaces four same-input rank-eight child calls by two, using four ADDs and four NEGs and no additional temporary. The affine map is checked symbolically over the integers and on 589,824 finite source/dirty-target cases; two omission controls fail.

Cost and limits

At the selected complex endpoint, exact rational outward enclosures give baseline lower 4 phi_8 > 0.4399830566696027 and candidate upper 2 phi_8 + 8 phi_1 < 0.3303711890451098, charging each added scalar gate one rank-one recursive unit. This is a scoped local mechanism and explicit surrogate cost screen. It does not establish that a selected supplier exposes the additive dirty-target contract, that the scalar-gate surrogate is its admitted price, that precision/tape bounds fit, or that the selected recursive profile or kappa improves.

This is distinct from PR #1410, which retains all ten children while persisting an order-four phase, and PR #1522, which shares a BIT source tour across outputs. The local Discussion claim could not be posted because GitHub GraphQL was rate-limited; the exact local claim and latest overlap status are in CLAIM.md.

Reproduction and verification

From repository root:

python3 -I -O -B research/dirty-output-delta-seed-b9eac2/verify.py
python3 scripts/research_package.py --package research/dirty-output-delta-seed-b9eac2 --check-only
make selected-record-check

All three passed locally on Python 3.14.7. The full research-package wrapper expects Python 3.12, which is unavailable in this environment; that replay and hosted CI remain pending. Source manifest pins the exact selected record, assembly, predecessor interface context, and rational-enclosure helper to base 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

Substantial OpenAI Codex assistance was used for scoping, algebra, implementation, exact verification, source handling, and exposition.

[Mister-Meeseeks]

Batch review at 84c68deb9fedc4c1695c7504502989d02d90fb24.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Symbolic dirty-output delta identity and exhaustive finite fixture halve child multiplicity for the stated same-input additive-child contract. The exact moment comparison uses an explicitly surrogate scalar tariff; selected-child exposure and precision/tape admission are unresolved.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.