[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. The exact #7113 caller has 94 literal idle calls. Its 90 narrow windows are pairwise disjoint. Every compatible group uses at least one of 32 total lanes from four broad signed idle calls. An exact nonnegative charge certificate covers all 1,361 groups: 366 pairs, 544 triples, 361 quadruples and 90 quintuples. All cases are resolved.

With one rank-additive shared child per group and free incremental setup, routing, phase, ownership, restoration, precision, tape and ordinary work, the complete savings upper is about 3.6413453744885866 raw units. The signed net upper is about −136.5436911891013 on the complete #7277 invoice at κ = 0.0040075385047236. The comparable benchmark remains κ = 0.003645669928698.

Task and overlap

Changed joint-query-controller scope at canonical base e545235. #7144 covers a fixed diagonal gauge. #7166 covers rectangular adapters, #1920 and #1924 cover encoding contracts, and #7207 covers fixed independent bases. The new proof prices the full compatible stock using the literal contact windows and lane capacities. This branch inherits the two exact #7257 CI prerequisites and adds one research package.

Validation

From a clean checkout with CPython 3.12 and assertions enabled:

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

Two compact inputs authenticate against exact public #7113 and #7277 source pins. The package reconstructs backward contacts and all groups, reprices the full incumbent histogram, and rejects changed input or a missing broad-lane charge. Registered, committed-source, navigation, and Git-free export checks passed. This scoped proof requires no new physical construction. The predecessor’s native, compiler and all-size gates remain separate.

Credit and open next question

#7113 supplies the caller, and #7277 with #7274 and #7244 supplies the complete price and retained native word. Credit #7144, #7166, #1920, #1924, #7207 and #6391 for related caller, stock and encoding work, and #7257 for the CI prerequisite. OpenAI Codex and subagents materially assisted the proof, implementation, independent audit and packaging.

A lower-than-additive rank needs a separate whole-stock price and an exact arbitrary-input gate. Changed contacts, new paid operators and packing two replicas of the same literal call remain open.