Prove conditional uniform R437 COPY contract and complete relative cost

[Clear1nsight]

This follow-up to #3936 proves a uniform local rank-seven COPY reduction for the nine current R437 frames and derives its complete conditional good/fallback bill. The requested uniform physical supplier proof remains incomplete; this package makes the missing integration precise and claims no admission or frontier change.

The new rank-specific Cauchy–Binet/Jacobi argument gives delta_7 <= min(1,448(q-1)/(q(q-2))) and <449/q for q>=450. Classification is shared by every high lift and unit ancestor weighting. The original plan pays 9872*f ordered ADDs on the good branch; fallback has at most 49911 main/half-reset children of width <=f. This yields T(7f,w)+delta_7*49911*max T(j,w), plus local scans and explicitly retained encoded preparation, under the stated completed-callee/refinement premises.

An alternate all-class exact-ring construction is also fully invoiced: one reversed 7f child, 41832*f ordered ADDs and 41832 ordinary interchanges. Those reverse-order adapters cannot be discarded or assumed to fit the original local tariff. The resulting failed implication is not an impossibility theorem against the original caller.

Validation: all seven registered Python 3.12 commands pass. New independent algebra covers all nine projectors and 45 modular contexts; independent nullspace and minor checks include 92112 complete small-GL matrices. Authenticated original plan probes and an actual encoded numerical-component probe pass. The latter uses actual COPY515 and a declared synthetic rank26 ancestor, 1664->182, four coefficients, restored program/prefix/numerical state and three rejecting source controls, with runtime host decoding disabled. It is not a full R437 Catalogue, payload/stock or physical CALL/RETURN test. Actual optimized Git-free CLI corruption controls pass. Receipts, source pins, command log and validation hashes are included.

PR3936 CI was checked first: initial run 39202988286 and current-head run 39205477701 succeeded. Current head e54c649 differs only by the P112 workflow repair; scientific bytes are unchanged. Canonical main 20ecf28 and revision-6 priorities were refreshed unchanged at checkpoints. This explicit donor task refines independent-moment. Claim: #3936 (comment). Overlap coverage is partial.

Credit: ai-nanachi/#3647, Sagar Thakrar/#3700, Ali Romman/#1043 and retained R437/native lineage; alephnan/#1627, Adam Gall/#2088, Ross Richardson/#1704 for complete streams; eumemic and Jose Manuel/#2234 for split bases/common labels; David Arias/#2753, Jose Manuel/jmbarrancoml/#2809/#2899/#2915, Nick Petalas/#2808 and retained physical/primitive lineage. zxv/#3690 already provides a finite R437 adapter and controlled rank34 return at older source 36ff441; our unchanged-selected-Catalogue 659/661 guard does not refute that adapter. Jose Manuel/#3562 and Sagar Thakrar/#3724 already supply conditional ordinary retuning/arithmetic checks. Full notices and Apache-2.0 license are retained. New proofs/code/checks by Chris R / Clear1nsight with substantial OpenAI Codex assistance; no independent human or formal-kernel review.

Next: refresh #3690's finite adapter at the current a24f9ff/OQ4 source, authenticate its actual rank26 ancestor and rank7 COPY in the complete physical ordinary/native/router cohort, then prove uniform preparation, continuation and visited-cell reserve. The local matrix proof and synthetic probe do not discharge that obligation.

Reproduce: python3 -B scripts/research_package.py --package research/r437-uniform-copy-reduction. No fresh selected cold replay or native rebuild is claimed.

Published commit 3647014 passes exact package/replay-input byte and source-history verification (29 new package files plus 25 canonical live inputs), package metadata/pins, and whitespace checks.

[Clear1nsight]

Upstream verification: run 39209275255 passed both plan (117918820681) and the explicit registered package replay (117919520786), including committed-input immutability. This confirms execution at 3647014, not mathematical admission. Claim released in the predecessor handoff; research-hub continuation. Uniform physical integration remains open as described above.

[Clear1nsight]

CLAIM — explicit donor follow-up: refresh zxv/PR3690 adapter (03c141e) to current R437/OQ4 a24f9ff; authenticate actual rank26 ancestor and rank7 COPY through the full physical caller. PR3950 CI checked first: run 39209275255 completed success, including registered replay and input immutability. Canonical main 20ecf28, revision6, unchanged. One approximately 60-minute session from 06:28 UTC, final quarter reserved for verification/handoff. Preserve frozen inputs; no frontier change. Success test is actual current catalogue/program binding, protected payload return and restored source/stock/scratch, not the previous synthetic rank26 descriptor probe. Any full-cohort obstruction or remaining uniform refinement/cost premise will be stated explicitly. Targeted R437 PR overlap and existing #1166/#2319 context checked; coverage partial. Claim expires 2026-10-19 08:00 UTC. Chris R / Clear1nsight with substantial OpenAI Codex assistance; predecessor credit retained.

[Clear1nsight]

DONE for this bounded session; claim released. Partial result published as #3967 at32af060614fefa9729c86370524c2e72265acd76. PR3950 CI checked first and green. Main20ecf2891d80b5acf18d980b2164fb44ea7faa90/revision6 remains unchanged.

Refreshed zxv/PR3690's source adapter to actual a24f9ff/OQ4. Full catalogue:28233 canonical/903456 paid requests, all7814016 literal controller events. Exactly seven records change (five MOVE owner routes; two IDLE ranks34/34->26/42), not just a histogram. New digest cbfea55f5cd0b74a2a0d4292ad0139d2b5bb73127951127698030bc90c73c532; stale digest rejects.

Actual IDLE27776 and COPY1603 now pass nested physical CALL/RETURN at2048->832->91 using the actual28416-family/660-stage-role inventory (29097 canonical stream roles). All63 literal private-result readers and disposal execute, with source/program/numerical restoration and explicit empty parking-stack/port checks. Five typed source/gate controls reject. The payload remains controlled46 bits in two23-bit fibres, stock11 and declared child outputs; no complete residual permutation, GL64 global macroprogram or production ordinary/native/router cohort is claimed.

RANK26-COST.md derives delta26 <=min(1,1664(q-1)/(q(q-2))) and the full conditional local bill, including13444f ordered ADDs. Rank7 retains9872f. A rank26 completed child includes a whole node, so it cannot be priced as only the sampled rank7 COPY inside it. All fallback/preparation/routing/stock/visited-cell premises remain explicit.

All five final registered commands passed in605.885 seconds, including normal/optimized physical and Git-free CLI controls. Exact158-file published-byte/canonical-source-history and whitespace checks pass. Upstream #3967 run39215291431 is in progress at posting. No merge, selected-frontier change or frozen-input edits. Credit zxv, ai-nanachi, Ali Romman, Sagar Thakrar, David Arias, Jose Manuel, ywz65, Nick Petalas and retained lineage; substantial OpenAI Codex assistance disclosed.

Next substantive task: use this current binding to prove the source-generic compile_node/Machine.run refinement and connect the complete production constructors at one catalogue, with admitted original-width stock, generated history/precision and full visited-cell reserve. Another controlled returned payload would not close that join.