[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. On the signed #7113 caller, replace one of four Type A QUERYs with the same-clock ordinary ADD and allow one of 17 J blocks to change. All 68 required phase differences have exact rank three. A rank-two provider cannot realize any of them through invertible q-even left and right adapters within the same port. All 68 changes also fail on the original four-role layout.

The complete #7277 invoice includes all 17 native copies and 96 Type A ports. The optimistic price gives 96 rank-one child credits per alternative before added charges. The compatible saving upper is zero, with zero unresolved cases in scope.

Task and overlap

Refines the P104 signed-caller scope at canonical base e54523517d0f03e58352e647c403a5af3e525a57. The exact comparator is #7277 at ed090b57ed88f8859e5ff4643645099e6ba856ea (κ = 0.003645669928698). The pinned #7113 caller head is 07a76c5e2738882c0cb322278e56f6cae3c9885d. #7309 keeps all J blocks fixed. #7144 studies body gauges and #2090 covers an older frozen itinerary. This package allows one changed J and measures the minimum required phase rank. The branch includes the two existing #7257 hosted replay prerequisites.

Validation

From a clean checkout with CPython 3.12 and assertions enabled:

python3.12 -B scripts/research_package.py --package research/p104-type-a-phase-rank-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-type-a-phase-rank-bound --check-modes --check-source-history

Registered, committed-byte and Git-free replays passed. Six navigation tests passed. The replay authenticates its inputs by path, rebuilds the directed price, verifies both signed endpoints, and compares the fixed-layout, rational-rank and modular-minor receipts byte for byte. It checks each modular minor entry and determinant against the exact rational calculation. Altered receipts and duplicate pin keys were rejected. The modular rank-drop control shows why a zero residue would require exact follow-up. No candidate construction or outer theorem replay was needed for the scoped exclusion.

Credit

#7113 supplied the literal signed caller and phase interpreter. #7277 supplied the native word and complete invoice. #7309 supplies the narrower fixed-J result. Round 45 supplies the rank-one transport. Round 46 adds rational rank and modular minor verification. OpenAI Codex and subagents materially assisted.

Open next questions

Choose one already-paid provider with a rank-three phase difference, pin one required matrix from the receipt, and price its arbitrary-input action and dirty restoration. Higher phase rank, multiple changed clocks and cross-port edits remain open, along with full physical and all-width admission.