← Skew Field / Experiment Rounds / Round 8
The fourth alternation cycle C₇→γ₈→C₈, establishing for the first time a “dual-pool” methodology: the dispersed lineage and the localized-penetration lineage each independently search for Fourier-18 candidates, with a separate non-Fourier B-spline held-out pool built alongside. This round also refutes three overly simple assumptions at once — that a localized lineage necessarily produces a localized phenotype, that a dispersed lineage necessarily produces a dispersed phenotype, and that a localized-penetration type is necessarily harder to absorb than a dispersed type — all fail to hold. The spatial-exposure phenotype is a joint function of curvature spectrum, spectral phase, congruence configuration, and container geometry; the absorption rate, in turn, is a relational quantity between the attack phenotype and the current container state — neither is a scalar property of the curve alone.
Relationship to other packages, stated as far as possible in the document's own words, not my interpretation. This case's theoretical foundation is in From the Original Kakeya Needle to Moser's Worm.
“The more accurate relation is: spatial-exposure phenotype = P(curvature spectrum, spectral phase, congruence configuration, container geometry). The absorption rate, in turn, is: η = R(attack phenotype, current container state). Neither is a scalar property of the curve alone.” — from Section 8, “New Theoretical Judgments,” of this package's main document.
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sha256 117d985ee98a579590630744e7c90e751ae523af63c13c7d5c76e4fd06d8523d