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DONE: Ordinary-algebra feasibility of the negative odd-E8 decoder #5503
JoyboyBrian
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DONE — contribution submitted: 5508. Maintainer review remains pending.
Exact head
7e6824d560337e2b2e49da8b98727183491f6ecf; 2 substantive commits. Local validation and independent agent review are evidence for this scoped contribution, not human or formal-kernel acceptance.The actual odd-E8 three-stage E caller still lacks its negative Gaussian decoder. This package derives the required postdecoder Q^-1 B_E^-1 Q and binds a nonzero path to the actual112^3-owner spectral code, rather than the source toy fixture or failed naive B_E^-1 decoder.
The attributed fresh-stage separation/contraction lemma gives ADD >= max(0,2f-216). More strongly, the complete columnwise monomial-Clifford algebra has at most2^8178 support maps per owner block; the actual decoder lies outside it for everyf>=4198, even with arbitrary instruction count and f-dependent scalar coefficients. Cross-column permutations retain only the ADD-count lower bound. Paid decoders, correlated histories and changed targets remain open; no new kappa is claimed.
Exact pending source56ba6d7d609124d71c067d6a380caed573963f8f is fetched and byte-checked at its immutable Git objects; it is not a publication ancestor, so the stricter source-history ancestor gate is not claimed. Frozen source attribution is preserved. The new contribution is the actual E spectral/path binding and its explicit native-alphabet consequence, not a new general path-separation theorem.
Validation: Python3.12 registered normal/optimized checks; exact spectral coefficients and signed25-axis sparse phase columns; repeated-stage/common-axis controls; copied-source, typed-receipt and strict-threshold faults; committed-byte checks and exact immutable source-object matching; official export; read-only Git-free full-manifest replay with unchanged bytes. Final export's16 scientific payloads equal the replayed export exactly.
Claim: #5503
Substantial OpenAI Codex assistance; predecessor notices and Apache-2.0 retained.
Claim base
32890bc5de034ab8fc93ac88ead7279a6a416d04. Selected frontier unchanged.All reactions