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research: screen rank-2 block helper inventory - #3896
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Summary
Adds a source-pinned exact screen for one proposed local helper contract: replace eight rank-1 scalar products implementing one complete 2-by-2 matrix product with one recursive rank-2 helper. The candidate changes the selected per-call profile and returns the six units of freed rank mass per block to the rank-51 idle remainder.
The best optimistic profile in this rewrite class (
t=301) has exact root bracket[2632122649/1000000000000, 52642453/20000000000]and complex kappa cap52642453/20052642453(about0.002625212768012246). The minimum count that moves the complex root past the selected bit root is 22 blocks per call. Even the maximum profile remains below1/99; with the bit supplier unchanged, the overall cap is about0.001730427469823603, below a 5% system gain over the selected0.001672660197076918.Scope and limits
This is an exploratory optimistic budget, not a source-mapped construction or supplier admission. It does not establish that the selected word contains any complete M(2) subword, and it omits extraction, frame, routing, addition, restoration, hosting, precision and consumer costs. No kappa or selected-frontier change is claimed. It is distinct from PR #3874's combined ideal-lever grid; related block/direct-sum and common-product work is credited in the package README.
Verification
python3 -B research/complex-local-word-ceiling/verify.pypython3 scripts/research_package.py --package research/complex-rank2-block-helper-screen --check-onlypython3 scripts/research_package.py --package research/complex-rank2-block-helper-screenThe exact receipt is
research/complex-rank2-block-helper-screen/RESULT.json. No full selected cold replay was run.Publication validation
python3.12 scripts/research_package.py --package research/complex-rank2-block-helper-screenpassed on CPython 3.12.3, andpython3.12 scripts/check_research_commit.py --package research/complex-rank2-block-helper-screen --check-source-historypassed. The registered replay left the worktree clean. This supersedes any earlier pending note above for the registered package replay; separate full selected cold-replay limits remain as stated.