The Third Non-Convex Alternating Cycle, Spatial Exposure Entropy, and the Fourier-16 Residual Attack

Connections · Connections

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 difficulty of a non-convex universal container has at least three distinct axes: total exposure, the spatial distribution of exposure (scattered lobes versus a localized deep gap), and the container's absorption rate. Attacks of the same magnitude can produce completely different container responses depending on their spatial distribution.” — from Section 9, “Theoretical Feedback,” of this package's main document.

Round 7 Core Content

The third alternation cycle, attack legality, the formal attack magnitude (four connected components), container response, spatial novelty, the ten-family activity ledger, the Fourier-16 residual attack, convergence diagnostics, theoretical feedback (three difficulty axes), next node (dual-objective attack).

Method

The formal attack continues from Round 6's residual candidates, the ten-family container's three-stage coordinate descent, the design of the spatial-exposure ledger (gap-box entropy), the Fourier-16 residual search pipeline.

The Third Curve–Container Alternating Response Cycle

Attack step, direct addition, container response values, a complete comparison table of absorption rates across all three cycles.

Convergence and Residual Audit

The area-increase sequence (not yet declining), the attack sequence (non-monotone), the Fourier-16 held-out audit, the design of a more sensible stopping criterion.

Separating Spectral Novelty from Spatial Exposure Novelty

The formal definition of gap-distribution entropy, a comparison of the spatial-distribution data from Round 6 and Round 7, the argument that spectral complexity does not imply spatial dispersion, the exposure-mode alternation conjecture.

Files · Files

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