[ToikY]

Change and scope

NO VERIFIED GAIN. Exact conditional κ change 0%. On exact #7334 with the signed #7113 caller, a J host that absorbs two QUERY demotions must supply relative phase-defect rank at least four. The retained J supplies two. One additional scalar one-return macro with phase-even wrappers raises capacity by at most one, regardless of its Clifford rank. Two rank-one top-ups consume the entire 192 raw saving across 96 Type A ports before setup and routing.

The separate erased-carrier check grants arbitrary linear maps preserving common phase/body fibres. A same-volume canonical rank-one or rank-two top-up fails the exact width-eight displacement gate. Rank two requires at least 96/77 of the field volume. Charging that volume makes the full margin at the incumbent crossing less than −46.77 raw even with ancillary work free. The proof states the rank-three and higher price bound and leaves enlarged rank-one packing and a redesigned helper that preserves its independent productive return open.

Replay

Exact comparator #7334 at aaeec8c0acf01e99a5f331ef363a698d9c084ace, κ 0.00364665195644, and signed #7113 head 07a76c5e2738882c0cb322278e56f6cae3c9885d. Use CPython 3.12 from a clean checkout:

python3.12 -I -B research/p104-retained-j-phase-provider-bound/replay.py
python3.12 -B scripts/research_package.py --package research/p104-retained-j-phase-provider-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-retained-j-phase-provider-bound --check-modes --check-source-history

Local exact contract and price, altered-caller rejection, committed input and mode checks, and official Git-free export passed. The branch carries #7257's exact shared planner repair. This contribution verifies the stated provider classes and includes no changed native supplier.

Credit and next question

#7113 and #7334 supply the signed binding and complete comparator. #7309 supplies the phase-defect lemma, #7343 the exact paired host rank floor, #7342 the one-return distinction, #7296 the erased-child displacement method, and #7298 the directed tariff. OpenAI Codex and subagents materially assisted. For a new interface, bind a specific physical layout and show how it supplies extra phase responses while retaining the independent productive outputs and positive full price.