[TennisBowling]

Scope and new result

For the generic five-source common-B mutable-source connector, the minimum over all finite correct restored Q/R/X words at equal complete Q/R price c>0 and source-XOR price x>0 is

min(72c + 4x, 74c).

PR1370 already proves four source XORs optimal at fixed ten queries/62 readouts, and the displayed minimum is already the minimum of known attainable bills. The new contribution is the unrestricted-count lower bound on this equal-price slice—not a new connector alphabet, path invention, price expression or multiplication bound. At the predecessor's abstract five-factor tariff c=38,x=2, the global minimum is 2744.

The proof uses even output-readout parity and paired-mask capacity to reduce every word with at most 72 map calls to the inherited fixed-count case. At 73 map calls, source/query parity forces at least two source XORs, giving the midpoint cost; all words with at least 74 map calls cost at least 74c. This covers unbounded word lengths without an expanded circuit search. An explicit 11Q/62R/2X split-edge control attains the middle face and is also optimal at x=c/2.

Evidence

The self-contained written proof and exact primary verifier replay the inherited 2,600 normalized nine-point exclusion, 945-pairing obstruction, and 8,421 short source-restoration projections; the two-X multiplicity reduction checks 3,003 necessary cases. Five root witnesses and their full five-factor dirty expansions are checked in the free noncommutative module on all 37/40 arbitrary incoming rows. The complete fixture invoices are 2744, 2760, 2812, 2812 and 2778. Twenty-four primary test groups pass normally and optimized, including noncommuting-factor/heterogeneous-map/source-return/readout/scratch failures and read-only source-export controls.

A code-disjoint verifier independently checks the finite dependencies using integer Walsh autocorrelation, endpoint matchings and source-column images, and independently reconstructs all five root words. It passes 7,400 full dirty-basis executions and 240 dense matrix fixtures, plus 38 strict CLI controls across normal/optimized Python. Eight generator-side mutants now reject before stored-receipt comparison. Independent mathematical and adversarial AI reviews found no remaining concrete issue. The registered four-command replay and clean-patch replay on refreshed main both pass; exact tested hashes and limitations are in VALIDATION.md.

Reproduction on Python 3.12, standard library only:

python3 -B scripts/research_package.py --package research/mutable-source-uniform-tariff

Contract, source pins and limitations

The theorem needs common exact B, temporarily writable and unobserved sources, generic correctness for every admissible exact A_m/B and dirty input, positive row length, complete restoration, and exactly the declared Q/R/elementary-X alphabet. Prices include per-call dispatch; shared fixed admission/preparation remains additional. Unequal Q/R or port-dependent prices, residual word-dependent overhead, cross-call fusion/alternative lowering and specialized maps are not covered. This is not a physical supplier or selected-construction admission, all-size outer theorem, new kappa, formal proof-assistant result, independent human review or hosted CI claim.

Started from main 410026dc5513b87db92ae98571d1d5984c69a983; fast-forwarded before submission to ef5f39403610d231a0c27e8a6b4f08c10209bcd6, with all relevant guidance, catalogue, selected record, helper and pinned input bytes unchanged. Revision-2 recursive-interfaces selection seed a5233575a2c1e99c2506293e5c2388a4 was not rerolled. TASK.json explains the complementary refinement of connector-alphabet-change; the scoped claim preceded implementation. A bounded final overlap refresh through 01:57 UTC found no same-scope claim; nearby online-delivery, second-root and coherence work has different hypotheses. No novelty guarantee is inferred from search absence.

Pending proof/witness sources: PR1340 f1dcab36fa63f8226f70dd07e26f44afb9d39b51, PR1370 8a9b633879b5bfe03400a6c09c31bae7568e6261; retained PR943 cf360b4b09b7d0419decdd6ac85421fefed55bdd. No predecessor executable is imported or package copied. Exact source identities, live-input bindings, commands, controls and unrun obligations are in the package. Only this new research directory is added; selected/frozen inputs and frontier are unchanged. No merge or closure is requested.

Credit

Published for tennisbowling with substantial OpenAI-assistant and isolated-subagent work in proof, code, review and writing. Credit Arham Tahir/PR1340/1370 for the paid source-shear extension, original witnesses and fixed-count bounds; Ross Richardson/PR943/934 for the read-only obstruction/repairs and dirty lowering; shhxera/CubeJerry/PR889 and Chafik Boukhalfa/PR628 for earlier mechanisms. Cumulative repository attribution is unchanged. New material is Apache-2.0.

[Mister-Meeseeks]

Batch review at 5c1f39788a0fc669b7e37e27785c63e85788c350.

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

Reviewed scope: All-count equal-Q/R tariff follows from complete count-case reduction and freshly replayed finite exclusions, with credited attaining dirty words and full leaf invoices. Unequal tariffs, word-dependent setup and actual supplier admission are excluded.

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.