[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. On the exact 36-role Type A port of #7113, replace two of four QUERYs by ordinary even ADDs and allow one of the 17 existing J blocks to carry the change. The complete 102-key pair-by-host test exhausted with zero unresolved. Each required host has an exact nonzero 3×3 relative phase minor at q = ±1 and unit body. Independently, the exact negative-identity endpoint and #7309 defect-slack inequality force host rank at least four in every case. A retained rank-two host fails before a physical build.

Price and replay

Exact #7334 comparator aaeec8c0acf01e99a5f331ef363a698d9c084ace, κ 0.00364665195644. Exact #7113 head 07a76c5e2738882c0cb322278e56f6cae3c9885d. The whole-bill one-pair relaxation removes 192 paid rank-one positions across 96 ports, with productive and J stock fixed. The optimistic two-disjoint price is 384 raw before setup and routing. The 102-case obstruction applies to one modified host and does not address a simultaneous multi-host rewrite.

Use CPython 3.12 from a clean checkout:

python3.12 -I -B research/p104-paired-query-host-rank-bound/replay.py
python3.12 -B scripts/research_package.py --package research/p104-paired-query-host-rank-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-paired-query-host-rank-bound --check-modes --check-source-history

All passed locally, including official Git-free export. The replay authenticates pinned source bytes, rebuilds the price, verifies the predecessor's exact endpoints, checks all 102 minors and rejects an altered caller. The branch carries #7257's exact planner repair at d2e54af81f9dda6487636b79d4964a2385d89b2b so the shared onboarding check reaches the package replay.

Credit and next test

#7113 supplies the signed caller, #7334 the complete comparison, #7298 the directed price, #7309 the predecessor endpoint proof and controls, #7310 the single-QUERY host problem, and #7342 the separate standalone paired correction. OpenAI Codex and subagents materially assisted. Next, price one explicit rank-four phase provider that preserves the original J body and all-width caller contract before choosing a host. Round 78 is tracked in #7111.