[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. On the exact #7113 caller, Type-B events 1339 and 2324 apply signed rank-9 and rank-64 phases on eight corresponding ports. With arbitrary linear setup and extraction and a block-diagonal parity-scalar erased-child action, one canonical rank-73 child requires at least 266287972320/206158430209 times one field’s volume. The phase-count proof applies to every positive integer tensor width of the retained phase cores.

At the upper endpoint of #7277’s independently certified crossing, the complete signed invoice can afford at most about 1.001365082990607 field volumes under volume-linear charging. The directed raw margin is at most about −166.904940310003 at the required volume, even with incremental setup, routing, ordinary work, restoration, precision and tape free. The comparable κ remains 0.003645669928698. One literal pair and all eight port layouts were checked.

Task and overlap

Changed joint-query-controller scope at canonical base e545235. #7166 covers rectangular adapters for native MOVE pairs, #7163 covers BIT reflection displacement, #1920 and #1924 cover reciprocal and clean-invariant Clifford encodings, and #7295 bounds whole rank-additive caller stock. This package gives a displaced-dimension and affordable-volume comparison for the exact signed Type-B pair under its stated erased-child contracts. It inherits the two exact #7257 CI prerequisites and adds one research package.

Validation

From a clean checkout with CPython 3.12 and assertions:

python3.12 -B scripts/research_package.py --package research/p104-idle-child-volume-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-idle-child-volume-bound --check-modes --check-source-history
python3.12 -B -m unittest discover -s tests -p test_research_current_status.py

The replay authenticates exact #7113 and #7277 inputs, reconstructs both windows, checks signed phase counts and all eight port layouts, and independently reprices three probes. Registered, committed-source, navigation and Git-free export checks passed. Wrong-sign, duplicate-axis, spectator, changed-source and changed-port controls are included. The optional full-word check reproduced the stored port projection from the exact public word. Full physical supplier and all-size compiler replay remain separate.

Credit and open next question

#7113 supplies the signed caller and physical binding. #7277, #7274 and #7244 supply the comparable invoice and native lineage. Credit #7166, #7163, #1920, #1924, #7144 and #7295 for related proof and scope context, and #7257 for the CI prerequisite. OpenAI Codex and subagents materially assisted.

A field-mixing erased-child action, a different canonical operator or a different volume tariff needs a fresh displacement and complete price. The smallest follow-up is one exact two-field erased action under the incumbent’s affordable carrier.