Construction: exact complex P111 COPY word with a smaller paid recursive moment

[aliromman]

The cost-63 P111 decoder is known, but its source access, asymmetric COPY
endpoint, exact phase frame and dirty restoration need a physical word. This
PR adds a complete finite complex decoder and an executable coordinate
baseline with the same 674 original streams and physical endpoints. The sole
nonzero COPY endpoint is processed last. All source reads, adapters, copy
lifetimes and three unused rank-nine helper tails are paid.

Review files: Proof and scope · Evidence · Source pins and credit.

The complete recursive profile changes from
896 H1 + 444 H7 + 238 H8 to
945 H1 + 497 H7 + 182 H8 + 3 H9. An exact uniform inequality proves a smaller
recursive moment for 0 <= b <= 1/256, including the selected complex
exponent at the pinned base. The candidate also costs 108 more AXPY scans,
126 more dyadic scalar multiplications per address, and 392 more adapter
scans. This is a construction and a recursive-cost comparison; it is not a
runtime gain, selected-supplier improvement, or new kappa.

The proof binds each logical event to its exact live Clifford frame. It proves
the complete physical map and its inverse transpose, including allocation and
disposal of the one temporary stream. Dirty helpers recover their logical
inputs at FULL, so their physical outputs are F times their initial arrays.
They are not claimed to have physical identity endpoints.

Validation uses exact rational replay of all 674 independent logical columns,
a separate integer-column interpreter, every native phase and child rank,
four whole physical executions on 512 complex addresses per role, and every
matrix column of the rank-seven COPY. Eleven broken-word controls address
compensation, cleanup, source access, endpoint order, helper tails, temporary
lifetime, phase and recursive charge. Three further controls reject a missing
receipt and Boolean or float substitutions for integer receipt fields. Normal
and optimized relocated replays passed, as did a changed-source rejection and
the selected-record check. The coordinator separately replayed a second dense
input in both candidate orientations. Reproduction is:

python3 -I -B research/shared-carrier-decoder/verify.py
python3 -I -B research/shared-carrier-decoder/test_controls.py

The exact Gaussian physical replay is finite. A written composition proof
supplies its all-input conclusion. The package gives a conservative quadratic
finite tape-route bound; it does not claim the all-size linear tape, rounding,
side-correction, external endpoint, host-owner or outer-assembly obligations.

The new work is confined to research/shared-carrier-decoder/ at base
8bddbee377e2f3ce1f1247196c4b290d55767d20. Selected and upstream files stay
unchanged. PR #717 and PR #968 receive credit for the complex decoder and the
copy-cost result; PR #620, PR #757, PR #761 receive related depth-one credit. PR #998,
PR #1008 and PR #1020 concern different structural classes and do not supply this
physical construction. The exact compiler is retained and pinned from
@icekylinx's PR #531 lineage. Prepared for Ali Romman (@aliromman) with substantial
OpenAI Codex assistance; Apache-2.0. No independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at d27499553138bde007f5b1163e65e71da1b18899.

This remains open after scoped triage. Next review step: The finite physical decoder replay reached 180 seconds. Finish all native signed-phase, complete physical-array and inverse-transpose checks before incorporating the physical construction; no defect inferred.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

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