Scoped negative result: orthogonal P120 shared-total pairs fail diagonals

[1337isnot1337]

Result

Scoped negative result; no exact decoder or new κ. This changes the relative root geometry from PR #1366's fixed odd-pair pencil e=L51,d0=L1 (<e,d0>=2) to the seed-selected orthogonal pencil e=L48,d0=L91 (<e,d0>=0). The ordered orthogonal partner is selected reproducibly as index 48 mod 63 in the sorted list of orthogonal roots.

The exact finite census tests all 120 targets and 511 nonzero sink words, retains 65 calibrated rows with nonzero target diagonals, and examines all 2,048 distinct-target pairs. The union correction total is available at both sinks for 1,056 pairs; every one cancels at least one target diagonal (1,024 cancel both; 32 cancel one). There are no exact pairs in this family.

The obstruction is exact: if target t_a belongs to the other row's required-total set, then p_e(t_a)=0, p_d(t_a)≠0, and the total subtracts p_d(t_a), making the required diagonal zero.

Why this family was tested

A successful unit with the same C.6 accounting would cost one rank-one shared total plus eight rank-eight coordinate totals, or 65 local COPY-rank units, against the P120 all-pairs floor of 72. The result rules out that potential saving only for this pencil and total rule. It does not cover other orthogonal pencils, uncalibrated rows, different total directions, multiple totals, or a complete recursive supplier.

Reproduce

python3 -I -B research/seed48-p120-orthogonal-shared-total/verify.py
python3 scripts/research_package.py --package research/seed48-p120-orthogonal-shared-total --check-only

The exact verifier replays PR #1366's odd-pair obstruction, the full P112 C.6 112-by-112 positive control, a required-total-source deletion control, and a label mutation control. Source/base pins are in SOURCES.json; proof and limitations are in PROOF.md.

Pins and credit

• Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f.
• Root/label source: PR Research: seed 51 P120 shared-total diagonal obstruction (no new kappa) #1366 head 21046cb8fa0d4f0e9b2f826ba71e01baaf9be02c; the certificate is vendored byte-for-byte and pinned.
• Local replay ran under Python 3.14.7 because Python 3.12 is unavailable here. The package manifest registers the standard-library replay for the repository's Python 3.12 runner.
• Credit Cinna Davis for PR Research: seed 51 P120 shared-total diagonal obstruction (no new kappa) #1366, PR Research: frame-pair decoders and the exact 8-term complex copy-cost floor (no new kappa) #968 for the P120 frame-pair floor, and the format-limits C.6 record for the 65-unit cost convention. Prepared with substantial OpenAI Codex assistance; no independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at cd29f533e8b1a9a9605bdabd8c0edff3ba1a6d7f.

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

Reviewed scope: Complete calibrated one-shared-total census for the selected orthogonal P120 pencil: every readable pair loses at least one required diagonal. Reproduces the odd-pencil and P112 positive controls; other pencils and multiple totals remain open.

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.