Derive and price fixed-owner joint P104 compensation

[Clear1nsight]

This study corrects the entire raw two-axis Gram product at one explicitly prepared physical cut, replacing the requirement to make each local shear separately equal to identity. It derives the unique fixed-owner total compensator, including the retained caller endpoint correction:

Cphys = [[Ar,(Ar Ac-I)T],[T^-1,T^-1 Ac T]] = U((Ar-I)T) S(T^-1) U((Ac-I)T).

The order of the port-dependent physical operators is retained. The factorization is division-free and three layers are minimal in the stated two-bank unipotent-shear alphabet. The four spectral sectors have det(C-I)=2,-11,-11,-24, so the repair cannot simply be omitted on an unchanged spectral sector. Neither fact is a native-tariff lower bound.

A concrete owned-copy route costs 32,448 rank-one copy transforms, 1,049,152 unit array additions, 21,632 private-copy halves and one peak additional private array. Under the inherited 208-call bare-channel/progress assumptions, even free joint repair has excess 832; this route has excess 33,280 before other physical costs. The general changed-profile necessary gate is C_joint < 10,816 - 208*(mass-progress). A changed completed local endpoint must rebind progress and preparation.

Scope: the caller supplies the physical chart convention, but an actual chronological P104 producer at the prepared cut, interstage alignment, opposite native orientation and helper-bank completion are not supplied. Dirty helpers are fixed through the repair itself. No source/consumer saving, runtime gain, global supplier or new kappa is claimed. This is an elementary symplectic-factorization/operator-algebra contribution; no external payload code or local Q/D consumer is modified. Native expansion stops at the failed named gate.

Evidence

Adds exactly nine files under research/p104-joint-compensation/. Public head 48e2e44d8785be8204d8c4b719850332f4f9abe0, tree 1ad70dbf7ab07e10cef2f7ed8950b3a8056ff6d9, canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90.

• Free noncommutative algebra checks joint endpoint and ordered physical factorization, without assuming the two Gram variables commute.
• Canonical roots reconstruct A^2=13A, the complete half-coefficient support and all 104 donor columns; the frozen word is recounted for mass/progress only.
• A separate implementation checks 32 literal Gaussian-integer columns and eight arbitrary dirty columns at noncommuting varying charts, with three physical faults.
• Fourteen actual normal/optimized CLI runs cover false/Boolean/float receipts, duplicate JSON and changed/missing sources.
• Python3.12 registered replay and exact-public-head byte/source-history preflight pass for 13 declared files. All three registered commands pass from the official read-only Git-free export, whose 14 files retain hashes and modes. Archive SHA256 0dab47769a36035016be60326bda5dd5ab6b0862c0fb4f7ea1a1a5197e0e6c07.

python3.12 -B scripts/research_package.py --package research/p104-joint-compensation
python3.12 -B scripts/check_research_commit.py --package research/p104-joint-compensation --check-source-history

Final-head hosted CI passes on first attempt: planning and package replay jobs succeed on CPython3.12.15, testing merge e23a792 of exact head48e2e44d into main20ecf289. All three declared commands and committed-input preservation pass. No inherited full native-channel replay, selected cold audit, human or proof-assistant review is claimed.

Selection, obligations and credit

Assigned changed scope under revision6 p104-side-correction. Canonical main was fetched at entry/before publication and remains unchanged; live latest-100 open PR bodies and the repository overlap helper were rechecked. Discussion/closed-PR coverage is bounded and coordinated through the stream's canonical claim. Concurrent payload coding, changed Q/D consumer and translated-progress studies are distinct.

The next useful task is one actual producer/repair fusion with all physical owners and a newly favorable complete invoice. Global scheduling, exact native phase/orientation, scalar/wrapper/routing/holding/control/tape costs, signed floors/precision/recovery and all-size supplier admission remain open or inherited. Selected frontier unchanged.

Credit Rohan Arun/#1972, Chafik Boukhalfa/#1991, Adam Gall/#1940, Chris R/Clear1nsight/#3882/#3940/#3943/#3954, 1337isnot1337/#3894, ToikY/#3956/#3966, #3961/#3962/#3965, and the retained E8/native/compiler/caller lineage named in README. Prepared for Chris R/Clear1nsight with substantial OpenAI Codex multi-agent assistance. Apache-2.0. No merge or closure requested.

Canonical coordinated claim: #3954 (comment)