The Second Non-Convex Alternating Cycle, the Absorption Coefficient, and the Fourier-14 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.

“Whether the container can absorb an attack depends on the geometric complementarity between the attack and the existing non-convex structure, not just on the attack's exposure by itself.” — from this package's main-document conclusion, contrasting the gap between Round 5's 57.7% absorption rate and this round's 9.5%.

Round 6 Core Content

This round's goal (directly continuing Round 5's held-out candidates), the formal attack, the second container response, active skeleton, comparison with Round 5, the Fourier-14 residual attack, convergence assessment (no evidence of monotone convergence yet), honest limitations, next node.

Method

The initial attack (directly reusing Round 5's held-out candidates rather than reselecting), the nine-family container response pipeline, leave-one-out design, the Fourier-14 residual attack search, honest limitations.

The Second Curve–Container Alternating Response Cycle

Complete numerical breakdown of the attack step, direct addition, and container response; comparison of absorption rate and novelty coefficient against the first cycle.

The Attack–Response Sequence and Convergence Criteria

Formal definitions of the absorption coefficient and novelty coefficient, numerical comparison across the two cycles, the list of quantities that must be monitored, this round's independent Fourier-14 held-out audit verdict.

Files · Files

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