Research: exclude single-child absorption with fixed stream encoders

[RossRichardson]

The concrete T740 idle-axis transfer child10 -> child12, axis16 has cheaper residual ranks 48,48 -> 47,49, but changes its physical operator. This package tests whether replacing one existing completed phase child can absorb that defect without an additional repair call.

It excludes all twenty residual sites for owner replica zero / port zero, even granting arbitrary invertible scalar stream-only encoding and decoding, any nonzero Fourier eigenvalue function, and zero added implementation costs. Nineteen sites have rank-two defects at character16. Site12 needs different rank-one projectors at characters16 and33554432; their flattened minor is -2i. Per-character rank and even commutativity would miss the latter obstruction.

The written normalization proof, exact cut witnesses, two separately constructed checkers and controls are in research/idle-single-child-absorption/. The adapters are explicitly L_stream tensor I_address. Address-mixing or character-dependent encoders, two changed sites, other transfers and changed words remain outside scope. No new kappa, supplier admission or selected-frontier change is claimed.

This closes a specific absorbed-repair question left outside PR3220; PR3229 addresses abstract independent-group sharing instead. Credit Gonzalo-Mier/PR3199, Nick Petalas/PR3187, Gareth Davidson/PR1387, Jeremy Diviney/PR3148, Rohan Arun, dcharb78, Dumitrean, Jeremy Kothe and the retained native/geometry lineage. Substantial OpenAI Codex assistance, including separately tasked mathematical specialists; no independent human or formal-kernel review claimed. New material Apache-2.0; frozen sources unchanged.

Validation at 897bfb42c389d24d2d54a381a216e1f876b42109:

• Complete registered Python3.12 replay passes, including both checkers and all controls.
• Independent arithmetic covers147 baseline characters and74 candidate characters at all20 sites; all1344 entries of the decisive matrices agree with the primary calculation.
• Optimized Python3.14 replay of both checkers passes from the committed Git-free export.
• All28 committed package/input files pass byte comparison and export-integrity checking.

Reproduce:

python3.12 -B scripts/research_package.py --package research/idle-single-child-absorption

Canonical main refreshed unchanged at 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision6. Pre-submission overlap covered294 open PRs including drafts and2074 Discussion records, complete pagination and no warnings; text coverage is not a novelty proof. Canonical investigation.