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This was referenced Nov 11, 2026
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Change and mathematical scope
On the exact selected #7001 native word, the nine owned summary rows project to a binary [111,9] code with minimum two-dimensional support 75 and 111 distinct nonzero columns. At the fixed target κ = 0.0040075385047236, generalized support and incidence bounds exhaust the six- and seven-summary profiles. An exact projected rank test over all 16,110 distinct rank-six chart pairs excludes the eight-summary profile and two nine-summary profiles. The follow-up closes the last nine-summary profile, with ten rank-six collectors and one rank-one collector. Every distinct pair complement has rank nine after any single-column deletion. Allowing an arbitrary extra line for each pair leaves zero compatible pairs.
The bound fixes the rational catalogue, monotone source support, retained summary rows and chart-zero descent interface. It overgrants arbitrary XOR recovery and timing. Smaller savings and changed source interfaces remain open. NO VERIFIED GAIN. The selected BIT saving and complete conditional κ are unchanged.
Task and overlap
Refines
bit-helper-contracton canonical basee54523517d0f03e58352e647c403a5af3e525a57. #7146 covers up to four summaries and the five-summary target case. This follow-up covers larger joint replacements using a different support and incidence proof. The exact selected live BIT word has blobb718d6b2848215ad785022106dfa9f871a3d1c0cand SHA-25651203e7fc75ba10bd3ac3f8e675759f47e13d262bea66b6600d1e515095cad78.Replay
Registered CPython 3.12.14, standalone, metadata and committed-byte checks passed. The verifier reconstructs the word, rational chart masks, code and profile receipts, and checks every single-column deletion via exact GF(2) elimination. The independent codeword replay checked 494 relevant codewords on each of 16,110 distinct pairs and found zero with uncovered weight at most one. The positive control becomes compatible only after allowing one extra line. The predecessor control and a separate 341-matrix rank and deletion test passed.
Credit and next test
Ali Romman’s #5421 supplied the owned relation mechanism. DreamingOfClouds, zxv, CubeJerry and retained authors supplied the selected native and paired controller. Codex and subagents materially assisted. A cost-neutral redirect of an existing public MOVE is an open route. It changes the monotone support premise and needs exact source availability, output equality, restoration and a fully charged physical invoice.