Conditional κ = 0.001274415506145115: paid complex kernel + rank151 target mixing

[rohanarun]

Conditional candidate κ = 0.001274415506145115, 0.03005550944143967% above #458. This composes #458's paid-adapter complex supplier with #459's rank151 target-mixed bit supplier, both unchanged and source-pinned. The bit side binds.

Submitted as a draft before full supplier replay, as requested. Both exact rational moment engines and the new six-level outer assembly already pass, including all47 strict inequalities, adjacent-grid rejection and invalid-parameter controls. This screen uses the pinned published supplier results; it is not a claim that the full parent wrappers have been freshly rerun. Full local verification has now passed on Python 3.11.15 and 3.14.8; GitHub CI is separate and is not claimed passed.

• Complex: 1297203880559577927527/10^24, from Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458 at 66f35b78d6fa32b2fea08765c2d6ae85e1c72fc3.
• Bit: 638020856745638414351/(5*10^23), from Conditional κ = 0.001266536148630309: rank151 kernel + target-prefix mixing on #451, complex-bound (+0.0477%) #459 at e037bc50c3d5efc1bec0d258a9f274f79ba45ec7.
• The seven shared upstream package inventories match exactly. Neither local word, geometry, ownership assignment nor supplier invoice is changed.
• Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458's explicit two-sided monomial corrections, one-helper-per-family-per-invocation rule and788480 paid wrapper groups are retained. No cross-family residual split is used.
• Conditional κ = 0.001266536148630309: rank151 kernel + target-prefix mixing on #451, complex-bound (+0.0477%) #459's155-bit prefix charge,520-bit three-level coefficient and complete19431 row coefficient remain; the complex20161 row contract is retained.

Reproduce: python -B research/complex-kernel-mixed151/verify.py /absolute/new/output. The default runs both original full supplier wrappers, rechecks exact endpoints and combined assembly, and binds both fresh receipts. The screen and fresh-full modes have distinct status fields. Source hashes, original notices, a proof of composition and Python3.11/3.14 CI are included.

All inherited compiler, target-label/mutable-basis, correlated-helper, restored-work, compressed-window, common-grid/tape, precision, row-divisor and analytic assumptions remain. This is a conditional composition, not an unconditional multiplication theorem or new Lean proof. The underlying target-label and paid-adapter arguments remain review points as in their source PRs.

Credits: chafreaky with OpenAI Codex for #458's paid-adapter complex construction; Rohan Arun with Claude Opus5.5 for #459's bit supplier; DreamingOfClouds for #449/#450 kernel and mixing work; DaysSky, icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman, Henry Grant and the inherited source-pinned authors. Composition and combined verifier by Rohan Arun with OpenAI Codex assistance. No independent discovery of either supplier is claimed.

Verification update: the initial full Python3.11 replay passed the complete PR454 chain, then stopped at PR458's absolute-tolerance comparison of inherited floating-point discovery metadata (gain estimate difference2.09e-12). A documented external runner normalizes only those two non-proof fields in a generated reconstruction input; pinned sources and all exact checks remain unchanged. The exact kernel reconstruction then passes. Failure and targeted repair evidence are retained; the repaired full replay now passes on both Python 3.11.15 and 3.14.8. Receipts, supplier receipt hashes and stage logs are in research/complex-kernel-mixed151-validation/python311-full/ and python314-full/. The Python 3.14 run completed as the full parent of PR462.