[flyingviper]

The eight owned transfers in the pinned PR5580 word cannot become cheaper through unchanged-producer rational recoding and direct delivery alone. This package classifies that family exactly and supplies a separate joint cost floor that allows arbitrary private sharing across all eight blocks. No new construction or kappa is claimed.

• All 511 binary hyperplane projections have exact rational rank eight except sixteen rank-seven cases. Their one-dimensional kernels are the eight original and eight mixed modes; every nonzero producer combination has original-entry support dimension at least eight.
• At each fixed final line, the three eligible mixed modes cannot reconstruct its original producer, even modulo arbitrary original zero-entry-input corrections. The receipt contains exact separators and an independence minor.
• Fixing the full 41-role public boundary, arbitrary internal rational dependencies and zero-initialized owned auxiliaries cost at least 31 H1(t) + 8 H7(t) for 0<t<=1. The source costs 33 H1(t) + H2(t) + H3(t) + 7 H7(t). The difference is only a cap on potential savings; attainability is unresolved.

The recoding result concerns direct nested 8-to-1 transfers from each mode's original-entry support hyperplane. The joint theorem excludes earlier preparation, outside public side information and new productive credits. Changed public dependencies and partial residuals remain open. Original-entry support is not treated as a free preparation recipe.

Files: README, proof, joint-boundary argument, receipt, source pins.

Validation on Python 3.12.14, standard library only:

python3.12 -B scripts/research_package.py --package research/p104-owned-coding-boundaries
python3.12 -I -O -B research/p104-owned-coding-boundaries/verify.py
python3.12 scripts/check_research_commit.py --package research/p104-owned-coding-boundaries --check-source-history

Normal and optimized exact checks pass, including every arbitrary-input scalar row, chronological frames and owned lifetimes, prefix/suffix ranks, seven information cuts, four semantic rejection controls and committed-result comparison. Full-history source checks, committed-byte checks and a read-only Git-free export replay with empty PATH pass. Two separate agents reviewed the classification/delivery and joint-cut arguments. No formal-kernel or independent human review is claimed. The unchanged native maps, physical caller, compiler and outer framework are not re-certified by this package.

Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, refreshed before publication; priority revision 7. Source: Ali Romman's PR5580 at 6efa248cf456d6101d757e9d09ba29711d18a13a, retained byte-for-byte with attribution in this branch's history. The package extends the sharing question left open in #5584. #5579's public-window obstruction is credited, not repeated as a new result. #5590 addresses fixed scalar contacts; this joint theorem permits changed internal dependencies under a fixed larger boundary. Discussions #5574 and #5575 cover adjacent retiming and compensated-source work. No selected record is changed.

Prepared for flyingviper with substantial OpenAI Codex assistance and independent agents; Apache-2.0. Retained credit includes Ali Romman, Joel Pulikkan/GamingPuzzled, DreamingOfClouds, thu-nmrc, Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan and the P104 source lineage detailed in inputs/README.md.