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Resolve PR6211's Gaussian-dyadic projector question with exact error 16193/65536. Preserve the real/complex and physical-cost boundaries. No new kappa. Contribution by Jerry Chen (@CubeJerry), with substantial OpenAI Codex assistance. Credit apoursh, Nick Petalas, Matarener and the retained P104 lineage.
This was referenced Oct 30, 2026
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Resolves PR #6211's dyadic-projector question: an explicit Hermitian projector over Z[i,1/2] has complex rank seven and maximum entry error 16193/65536 < 1/4 on the same 104-root Gram matrix. This removes odd denominators; it does not beat the predecessor's best complex error. No new κ.
Base: 2485805. Predecessor #6211: 369ad15. Published proof, exact input pins, search coverage and validation. Only this package is added.
Reproduce with CPython 3.12:
python3 -B scripts/research_package.py --package research/p104-dyadic-rank-sevenExpected: PASS_REGISTERED_RESEARCH_PACKAGE.
Executed on Linux/Python 3.12.14: six registered normal/optimized checks; all 10,816 entries in each of two arithmetic paths; exact rank and dyadic checks; nine semantic and four source-byte rejection controls. Six Git-free/read-only replays agree, and two actual exported-byte corruptions reject. The bounded search stops at its first witness (k=8); no denominator/error optimality is claimed. Remote commit/tree and all 14 package/input files are checked against tested bytes.
The P104/root identification is inherited. Real-part rank remains eight; residual spectral norm remains 13. Native realization, caller, residual correction, dirty restoration and a favorable complete invoice remain open. The selected frontier and five framework assumptions are unchanged; no full multiplier or formal proof is claimed.
By @CubeJerry with substantial OpenAI Codex assistance. Credit apoursh (#6211/#6191), Nick Petalas (#6183), Matarener (#6166), and the retained P104 lineage. Apache-2.0.