[ToikY]

Change and mathematical scope

Price the new class-three UT4(F2) central-target alphabet with arbitrary finite restored dirty workspace and every nonzero binary rank-one scalar coupling, including nilpotents. Every full formal word for w central targets requires n_a,n_c >= 2w and n_b >= 3w+[w=1]. The complete positive uniform tariff is at least 2w(alpha+gamma)+(3w+[w=1])beta; the explicit upper word costs 2w(alpha+gamma)+4w beta. One target is exactly eight calls; two targets lie between14 and16.

The new step combines a middle ker(X)/im(Y) quotient with degree-three mixed coefficients forcing both middle spans to have rank w. PROOF.md supplies the uniform rank argument; quotient.py certifies its fixed17-dimensional homomorphism lemma on all4,096 group products. A separate construction attains the necessary four-matrix relaxation for every w, without claiming a chronological word. Full endpoint acceptance uses the formal group algebra and an independently implemented faithful regular operator.

Only research/ut4-central-tariff-relaxation/ is added (13 files). This is a scoped lower theorem/relaxation, not a physical supplier, rational-frame identity, multiplication theorem or new kappa. The selected frontier is unchanged. Full multi-target optimality, proof-kernel formalization and physical/compiler/hosting/precision/tape/analytic transfer remain open.

Task and overlap

Base main c24fb5e. Revision3 task bit-new-register-model, nonce825a224ec7f742d396fd07c46cd8f17c, scope7084092dd726e7ba1f2f; refined to the specified nonabelian-family variation and target-specific relaxation method. TASK.json and SOURCES.json record the card, exact source bindings and limits. Claim and handoff.

Entry checked591 open PR bodies including drafts; pre-submit numbered pagination found532 distinct open PRs with no UT4 match. Main changed during paging, so this is not an atomic snapshot. The helper searched local metadata/ledger; live UT4 Discussion search found only our claim. Full Discussion pagination and all code diffs were not covered; no novelty guarantee. Guidance/catalog/selected/model blobs were rechecked unchanged at2de86c77b4127d2f01f504e0c7c5e4db737caa3c and again before publication at a18b4b0.

Validation

Run python3.12 -B scripts/research_package.py --package research/ut4-central-tariff-relaxation. Final registered replay passed in34.38s on Python3.12.14/macOS26.5.2 arm64 with standard library only. Optimized isolated verification passed;20 research workflow tests passed; staged whitespace check passed.

Exact finite evidence:30 full formal/faithful witnesses and7,040 basis columns;729 expanded ordered pairs;19,683 three-factor coefficient cases;128 attained factor fixtures throughw64;4,096 quotient products/4,913 algebra triples; separate literal4,096 group products/262,144 group triples and42 rank-one factors. Eight test groups cover actual failed words, omitted calls, dirty restoration, nonfaithful common kernels, source/receipt corruption, illegal domains, occupied outputs and read-only optimized relocation. VALIDATION.json records omissions. Finite role fixtures do not establish the uniform theorem; its written rank argument uses only the separately scoped fixed-group lemma. Selected cold replay was not needed or run.

Credit and next question

Credit steph4n-gh/#1573 at0b8c5a69297c794f2de22c04494c83e41300ae36 for all-register UT3 zero-sum ranks; Arham Tahir/#1589 at010ec8c01c0edbbb08b541be236ab78d096f2ca1 for nilpotent couplings; Hanson Sun (@bbMisk)/#1607 at9d6117918025cee6a0c5b7ef30ff8d936ca0621f for coefficient-span tariffs, plus retained lineage listed in README. No predecessor executable is imported and no literature-priority claim is made. Apache-2.0; prepared for @ToikY with substantial OpenAI Codex assistance, including two bounded subagents. No independent human or kernel review claimed.

Next: decide whether two central targets attain14 calls, starting with six middle factors whose two spans have rank two, then imposing chronological and full formal endpoint conditions. The relaxation provides headroom, not an implementation.

[Mister-Meeseeks]

Batch review at 01cc02b164ecc4f9d84df3f56a1fe65b88daf390.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: UT4(F2) central-target tariffs with arbitrary dirty workspace and rank-one idempotent/nilpotent couplings. Written natural/contragredient and degree-three quotient arguments give 2w/3w+[w=1]/2w counts; one-target eight-call optimum, multi-target relaxation not a chronological construction.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

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