Research construction: exact Hadamard price envelope and 222-call word (no new kappa)

[1337isnot1337]

Status: research construction and exact finite census; no new κ.

PR997 samples signed four-source/four-output Hadamard connector paths and finds a 22-query, 238-primitive word. This contribution exhausts its eight-source-call class, allows arbitrary repeated readouts, and finds a 24-query word with 222 primitive calls, using the same four dirty scratch rows. The new word executes 66 internal echo nodes versus 72. Every child and literal inverse is included. This is an exact interface operation-count comparison, not a measured multiplication-runtime improvement.

The completed census covers all 40,320 signed source orders. Two independent integer algorithms agree on all 114 minimum-profile frequencies and 22 Pareto profiles. The scoped minimum query count is 22. For positive complete A-query prices sorted a≤b≤c≤d, the exact readout-price envelope is 4a+4b+2c+2d+min(2c,4a); source queries add twice the sum of B prices. A 24-query word is optimal when c>2a. Higher dispatch or placement charges can change the winner, and the complete recurrence and an explicit reversal control retain that expense.

The domain fixes one positive and one negative B call per source, distinct sources and outputs, one arbitrary dirty connector, and exact linear additive children. The optimum requires the coefficient identity for independent formal operators; special maps with additional algebraic relations are excluded. The readout bound is justified by the four available coordinate differences, so arbitrary integer readout multiplicities are covered. Additional source calls, output borrowing, other query alphabets, rounded children and state/placement-dependent prices are outside the optimum. No supplier hosting, new recursive moment or new κ is asserted.

Reproduce with Python 3.10+ and the standard library:

python3 -I -O -B research/hadamard-readout-census/test_package.py

Expected: PASS_HADAMARD_READOUT_CENSUS ... leaf_calls=222_vs_238 ... no_new_kappa, followed by PASS_HADAMARD_READOUT_PACKAGE regeneration=PASS relocation=PASS controls=4.

Validation includes all 22 attaining words and the matched predecessor, free noncommuting dirty-state maps and inverses, 16 individual signed child contracts, 624 dense basis/dirty replays, 1,296 rational price fixtures, common finite-domain prefix/width bounds, ten mathematical controls and four actual subprocess rejection controls. Certificate regeneration is byte-identical and optimized read-only relocation passes. Selected-record integrity and all 25 related repository tests pass. Submitted Git-index bytes are replayed; exact receipts and primitive digests are retained. Full repository regeneration, cold selected-supplier replay, hosted CI and human peer review are not claimed.

Exact base: ce7ad1b6ab09452c3478723a2e96ed5ff212dc08; OS-random assignment seed 55, recursive interfaces. Only research/hadamard-readout-census/ is added. The reviewed PR1094 selection and upstream/ remain unchanged. All-size/compiler, realization, hosting, precision/tape, exact recovery and analytic transfer obligations remain.

PR997 is pinned at b3fda8d59436103b195069a6328cbf5d74f73bc0. Credit also remains with Martin's PR1088 weighted 3x3 repair, CubeJerry's PR889, Ross Richardson's PR934/943/944 and Chafik Boukhalfa's PR628 echo lineage. Original notices and source bytes are retained; no predecessor executable code is imported. This is a new independent implementation extending the same contributor's earlier PR997. The refreshed 767-open-PR inventory through #1152 found no competing exhaustive 4x4 arbitrary-readout census. PR1103 uses rectangular output borrowing. No pinned sprint issue exists, so the claim and result handoff are local.

Prepared by Cinna Davis (@1337isnot1337) with substantial OpenAI Codex assistance in research, implementation, verification and writing. Apache-2.0; no full multiplication-theorem or unrestricted optimality claim.

[Mister-Meeseeks]

100-PR batch review at 6336d879c0ba168463bf2f6fae9e653c870299fc.

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

Reviewed scope: Complete signed Hadamard readout census, weighted price envelope and 222-leaf emitted word under the exact borrowed-child contract.

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.