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Prepared for @CubeJerry with substantial OpenAI Codex assistance. Credit CrocSwap#6766 for the shared endpoint and broader all-size ceiling. No new kappa.
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Give a distinct four-query word with the same six-input endpoint as #6766: 20 literal events instead of 21, or 22 instead of 23 after identical final normalizers. A four-input variant uses 18 events. Full q^4 coefficients and characteristic-two transfer agree. Event counts imply no weighted physical-cost saving.
Independently confirm the existing COMPLEX ceiling 0.0033072446849 with directed integer square roots and a separate rational atanh/Taylor checker. #6766 receives priority for the shared endpoint and broader COMPLEX+BIT result.
Base: 7c49fe3.
#6726: 435bbe9.
#6764: 1153341.
#6766: d87e4a3.
Exact retained hashes and unchanged notices: SOURCES.json.
Reproduce (Python 3.12, stdlib):
Expected:
PASS_BINARY_EQUAL_ORIENTATION_FRAGMENT_PACKAGE,PASS_INDEPENDENT_ATANH_TREE_REVIEW,PASS_REGISTERED_RESEARCH_PACKAGE.Executed: exact 4/6-input maps and inverses; all 20 event omissions; phase, alias, normalizer, source and missing-query controls; 44 finite totals and an analytic unbounded tail. The independent engine includes 2,352 orientation comparisons and 15,180 triples. Positive local-gain controls prevent overstating the obstruction. Normal/-O, metadata, committed bytes/modes, export and Git-free checks pass. No randomized construction search.
No new κ. Fixed native tariffs, root and independently paid idles only. Physical installation, changed idle-sharing interfaces, roots and native tariffs remain open. All five selected assumptions remain.
By @CubeJerry with substantial OpenAI Codex assistance and separate mathematical/arithmetic review. Credit Cinna Davis, Ali Romman (#6398), thu-nmrc (#6716/#6717), zxv (#6726), and #6764/#6766. No human/proof-kernel acceptance.
Proof, comparison and limits: https://github.com/CubeJerry/integer-mult-bounds/tree/a8dcada906c0b6e4bd0bba171ae45a5271a80cd4/research/binary-equal-orientation-fragments
Complete remote Git tree matches the tested contribution.