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Resynthesize P104 scalar prefix: 3,577 fewer events (No new κ) - #6116

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CubeJerry:research/seed31-p104-prefix-synthesis-20261028
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CubeJerry:research/seed31-p104-prefix-synthesis-20261028

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Replace PR6030's first scalar block by exact whole-matrix dyadic synthesis: 9,895 -> 6,318 events. The complete word falls from 22,803 to 19,226 events; local scalar allowance falls from 189,428 to 142,778. All arbitrary-input endpoints, ordered non-scalar events, storage and recursive profiles stay unchanged.

New scope: the entire 567-role prefix on selected PR6030, beyond #5975's peepholes and #5999's two-output window on PR5907. Classical row sharing/elimination is not claimed as new.

Base: 721c038 (canonical main re-fetched before publication).
Verified fork head: 815dd98; complete remote tree equals the tested tree.
Source WORD SHA256: 7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f.
Python 3.12.14, standard library only. Exact source/checker pins, proof, seed/domain/stopping rule and complete costs: research package.

Reproduce:
python3.12 -B scripts/research_package.py --package research/p104-prefix-row-synthesis
Expected: PASS_P104_PREFIX_ROW_SYNTHESIS twice, then PASS_REGISTERED_RESEARCH_PACKAGE.

Executed: normal/-O registered checks; independent dense integer prefix equality (321,489 entries); full 799-row/column word checks; explicit dyadic fixture; sign, SCALE omission, chart, denominator, unavailable-source, owned-zero-specialization and source-corruption controls. Committed bytes/history/modes, official export and Git-free empty-PATH normal/-O replays pass; damaged result receipts reject. All export bytes/modes remain unchanged.

No new κ. Local circuit result only: no full native/caller/compiler/precision/outer cold replay, supplier adoption, optimality or measured runtime claim. All five framework assumptions remain; no rounded multiplier is materialized. Hosted CI and independent human/formal acceptance are unclaimed.

Prepared for @CubeJerry with substantial OpenAI Codex assistance; no subagents. Credit DreamingOfClouds (#6030/#5907), Ali Romman (#5827/checkers), Matarener (#5975 handoff), Nick Petalas (#5999), Mason Hale (#5811) and retained lineage. Apache-2.0.

Exact arbitrary-entry matrix and complete local word checks; scalar allowance
189428 -> 142778. No new kappa. Prepared for @CubeJerry with substantial
OpenAI Codex assistance; predecessor credit and source pins in the package.
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