[dillona]

A nonzero pivot can still have a forbidden reciprocal. On exact #7123, the helper basis emitter retained d639=−7867/16 and rejected an affordable rational split. Swapping it with the cocharted unit d802=3 makes the construction legal in the existing alphabet and raises conditional κ to 0.003642219284637, a gain of 0.000000979634453 over #7123.

At cut after event 37583/chart 1027/pivot 639, a rank-nine helper splits into 5+4. The boundary/cut bases have lengths 426/17 and add 880 ADDs + 6 SCALEs, one independent helper and no paid-profile change. The declared neutral placement leaves every source instruction unchanged before splitting. The complete signed 17-stage application has 110,655 paid positions, 22,308 productive fields, surplus 1,424 and zero empty credit.

The freshly derived native grid needs 1125/F25, and F24 is rejected. Both precision paths carry this increased binary height through the complete application: c=2362, ordinary source-unit work 779,122,208 < 10⁹, and freshly counted physical/fixed-tape costs. Ordinary source units are distinct from machine steps.

Both complete direct CPython 3.14.7 commands and the final registered isolated CPython 3.12.16 replay passed. Every frozen native and composition receipt field matched. REPLAY.txt preserves the actual output; metadata was marked completed afterwards.

Coverage includes complete source/candidate reconstruction, arbitrary-input forward/adjoint, three 512-column boundary checks, finite native/signed routes, 17 corruption/grid/unit controls, the exact rational/integer Laurent caller, every 3,048 paid/helper chart maps and 104 main boundaries, owner/phase bindings, fresh grids/envelopes/costs, both exact price engines, a crossing-probe rejection and 54 strict plus four functional outer conditions. VALIDATION.md describes the grid adapters and exact coverage.

The complete 30-file #7123 export at 020d581d9856b6db83e448c3f20418bc63b72c34 is frozen with all nested sources/notices. The new native word is a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2. Both engines reject the predecessor invoice at the new claim. The independent raw crossing is (0.00364221928463783897927791107627154, 0.00364221928463783897927791107627155), a bound for this invoice, not all constructions.

python3.12 -B scripts/research_package.py --package research/p104-nonunit-pivot-split

The refreshed overlap check found Rohan Arun's #7124 output rechart at 97dc14132da53562b7939776d7a83d72af72eeb1, κ=.003641428753638. This claim is higher by .000000790530999, but composition with that separate result is unproved and listed as an open next question. Frozen #7123 inputs are preserved. Discovery selected one of eleven repaired rational nominations; no exhaustive rational optimum is claimed.

Five inherited assumptions, independent human/formal review, maintainer admission and compiled top-level execution remain. No selected-frontier change. Hosted CI is separate from local evidence; the existing canonical guide6030/selected7000 onboarding failure is outside this package-only change.

Credit Ali Romman for the basis/split identity; dillona/OpenAI Codex #7112 for the earlier zero-pivot smooth swap; Jerry Chen/CubeJerry, Matarener, Rohan Arun (#7122 rechart and #7113 caller/application), 1337isnot1337/OpenAI Codex (alpha-expansion rechart method), ToikY, DreamingOfClouds, Douglas Colkitt/#7000 reviewers, and all retained source notices. Substantial OpenAI Codex assistance; no subagents. Canonical investigation.

Exact-head hosted run 42910222708 failed the onboarding navigation test: 760 tests, 1 failure, 24 skipped; guide #6030 versus selected #7000 in test_current_ci_section_matches_selected_record. The scientific replay job was skipped. This is separate from the successful complete local registered evidence.