Non-Convex Area-Exposure Tension and the First Curve–Container Alternating Adversarial Cycle

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.

“This round directly quantifies, for the first time: curve attack pressure → container-reconfiguration absorption → net container increase. Result: roughly 57.7% of the initial exposure pressure can be absorbed by reconfiguration…so computing only ‘the new curve's exposure against a fixed container’ overstates the long-run area increase of a universal container; the container's response must be accounted for first.” — from Section 9 of this package's main document.

Round 5 Core Content

Research shift (from convex support gaps to non-convex area-exposure tension), definition of area-exposure tension, the Fourier-12 attack curve, multi-branch placement audit, direct addition versus defensive response, final container, active skeleton, held-out sample testing (not yet converged), this round's theoretical signal, honest limitations, next node.

Method

Defensive container, the Fourier-12 curvature family, search stratification (clearance-field screening plus tube-exposure recomputation), container-update pipeline, high-resolution replay, held-out sample design.

The First Curve–Container Alternating Response Cycle

Attack step, direct addition, container response, complete numerical breakdown of the recovery ratio and net increase, list of active families.

Clearance Fields, Morphological Erosion, and Area-Exposure Tension

Morphological-erosion formulation of the thickened-curve containment condition, why a polygon negative buffer cannot be used directly, the precise definition of area-exposure tension, the division of labor between the fast proxy and the final recomputation.

Files · Files

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