Save four ADDs in an actual BIT shared-source packet

[RossRichardson]

Summary

An exact factorization of one frozen R438 prelude reduces 13 ADDs to 9. The complete word uses 36,001 instead of 36,005 ADDs, preserving all 2,913 recursive queries, rank mass 5,101, nine COPY/ERASE episodes and the original expanded cleanup.

This revision also fixes the independent verifier's initialization of prefix metrics for a supplied nonidentity state and directly checks both inverse composition orders for every compared word. A focused regression reproduces the old undercount. All previously reported mathematical receipt fields and prefix values are unchanged.

Scope and limits

The two original queries act on distinct helper registers and commute as whole-register operations. Their address projectors do not commute: (PQ-QP)[0,1]=1/8. The revised prose makes this distinction and the scalar rewrite's entering cut explicit.

Source-only tours cannot transform the independent helper dirt required by the frozen interface. The displayed exact repair adds four rank-two queries; this is its invoice, not an optimal-repair or general noncommuting lower bound. The scalar saving has zero recursive-query moment delta. The public shear is Boolean; the signed lift preserves inherited even dirty-target terms.

Only research/bit-shared-source-compensation/ changes. The user-assigned scope differs from the pinned bit-new-register-model card, as documented in TASK.json. Scientific base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. No new κ, native supplier admission, all-size precision theorem, selected-frontier change or formal-kernel proof is claimed. Proof, receipts and open questions.

Test plan

python3.12 -B scripts/research_package.py --package research/bit-shared-source-compensation
python3.12 -B scripts/check_research_commit.py --package research/bit-shared-source-compensation --check-source-history

Registered normal and optimized Python 3.12.12 replay, committed-byte/source-history checks, and the official export integrity check pass locally. Only this package is selected for replay. Hosted Registered research packages CI passed on revision 5a34918402ae2c0c683d8820ad832970e77f6382, including both registered modes and the unchanged-input check.

The replay covers all 660 independent integer columns, actual frame projectors, delivery cuts, COPY/ERASE equality guards, both inverse orders, complete invoices and defect controls. Fresh separate algebra and verifier reviews found no remaining scoped defect; they also independently checked the nine-role scalar identity and the published prefix maxima. This is AI implementation review, not independent human review.

Sources and credit

The bundled WORD and GEOMETRY archives match #4021 at c01f97ecfc7fa64847f6abd8f7b231e1df8c7b70 byte for byte. Retain Ali Romman's R438/#1043, Sagar Thakrar's transport and hosting lineage, cheesegrader's #540 framework, #589/#1023 hosting and the controller contributors in SOURCE-NOTES.md.

Hanson Sun's #1522, building on Ross Richardson/#953 and Wentao Li/#840, already supplies additive-output source tours; the present dirty-helper obstruction does not refute that interface. Chris R / Clear1nsight's #4005 concerns a different R437 carrier-deletion quotient. Exact pins, attribution and the dated overlap search's limits are retained in the package; no novelty certificate is claimed.

New work by Ross Richardson with substantial OpenAI Codex assistance in derivation, implementation, writing and separate AI review. Apache-2.0.