Bound one-child COPY echoes with linear body ADDs and price fixed repair

[Clear1nsight]

PR3982 reduced the all-class rank-seven COPY's ordinary-call constant to196 but retained a positive upper-tariff scaling gap. This package tests a changed mechanism: remove ordinary interchanges through linear ordered body-address ADDs, arbitrary coordinatewise Boolean dirty echo, and one standard reversed child. That linear-address one-child class is insufficient on the full cube. A fixed two-rank-seven replacement also fails the exact current paid moment before cleanup costs.

The proof pairs local-ring projector geometry with time-unrolled circuit dependency. A path through one chronological child execution has address word in U or U W_l U, even with arbitrary dirty payload roles, nonlinear pointwise gates, masks, fanout and role reuse. For n=64f, output address e_n cannot depend on any source bit with leading index n−1 when l<n. A valid all-class rank-seven projector on indices57..63, with arbitrary unit ancestor weights, requires precisely that dependency. One proper-width child of any width, including42f, fails this witness. Global payload-dependent control or a new address-mixing scan would change the hypothesis. Affine translations/header-to-body constant additions are explicitly outside the linear U alphabet; the orbit invariant does not exclude those enlarged mechanisms.

The source profile has2592 COPYs and mass deficit10272. Replacing every COPY's one rank-seven child by two adds18144 rank mass: the optimistic moment at zero is9513/9472>1 and remains above1 for every nonnegative saving exponent. The one-child theorem does not imply a14-rank lower bound for arbitrary escapes: mixed child widths and adaptive schedules remain open. For an adaptive extra rank-seven call, theta<107/189 is only the zero-exponent necessary condition; the witness does not establish actual class density. Existing63-reader sharing is already paid once per private residual. Constant fanout and packing independent operand volumes do not remove the remaining upper-tariff gap.

The standard-library checker binds the exact R437 word and reconstructs36 GL64 conjugacies from all nine literal captures over Z/3,Z/9,Z/25,Z/289. Four complete small-cube dependency closures, a complete81-address nonlinear dirty-helper witness, full-width/extra-child controls and exact profile arithmetic pass. Normal and optimized registered checks pass, as does an actual Git-free read-only export with four source/invoice rejection subprocesses. All six retained inputs match their original Git objects byte-for-byte. This is a scoped all-parameter proof plus finite tests, not independent human or formal-kernel acceptance.

The complete obligation ledger retains source preservation,63 dirty consumers, clone/transfer/release/disposal/head-return scans, coefficient preparation and fixed-inventory lifetime backing. Unknown physical costs are zero only in the explicitly optimistic rejection. The general amortization exponent is(alpha+beta)p−alpha; the proposed R437 selector specialization is conditional and distinguished from the original ordinary width. No new kappa, source compiler, full supplier admission, selected cold replay, merge or frontier change is claimed.

Only research/r437-copy-echo-budget is added. Reproduce: python3 -B scripts/research_package.py --package research/r437-copy-echo-budget. Canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90 and priority revision6 were refreshed unchanged at entry and submission. Explicit donor parallel continuation refines independent-moment; the source card, changed scope, pins and open questions are included. Team claim: #3967 (comment). Local overlap lacked usable remote PR/Discussion cache; live COPY echo/commutator searches and parent coordination are bounded coverage, not a novelty certificate. PR3995's pooled-IR boundary and PR3989's transfer-lifting warning are complementary context.

Credit ai-nanachi/#3647; Ali Romman/#1043; Sagar Thakrar/#3700/OQ4; eumemic, DreamingOfClouds, Crow, DaysSky and chafreaky; zxv/#3690, David Arias, Jose Manuel/jmbarrancoml and the physical caller lineage; the donor's #3936/#3950/#3967/#3982. Rohan Arun/#3959 and its #3995 IR follow-up, and Gonzalo Mier/#3975 with the credited #3989 transfer lineage, retain their separate context credit. Full predecessor notices are retained. New work by Chris R/Clear1nsight with substantial OpenAI Codex assistance and separate same-session AI review of the dependency argument. Apache-2.0.

Final head 99a6320aa2299433f2fa3731de624ecbe1debe46 passes exact16-file publication-byte/source-history and fresh-checkout comparisons, retained-source identity, whitespace, and all three registered commands after the explicit affine-operation caveat. Hosted CI is reported separately.