Mixed Polyline–Curvature-Arc Families, Curvature Concentration, and the Value of Discrete Kinks

Connections · Connections

Relationship to other packages, stated as far as possible in the document's own words, not my interpretation.

“The discrete-event skeleton concentrates the total turning angle at the kink between the two segments; the constant-curvature wing, by contrast, spreads that same turning angle across the entire side wing … the effective factor may not be ‘whether or not curvature is present,’ but rather: where the curvature is concentrated along the curve's parameter.” — from Section 7, “The Curvature-Concentration Working Proposition,” of this package's main document.

Round 7 Core Content

A results table for piecewise-curvature wings (comparing five segment counts), the necessary search audit (a warning that the heuristic search did not recover the known control solution), the analytic contour of the continuous constant-curvature wing, the final ranking table, the curvature-concentration working proposition, points where the results should not be over-generalized, a resolution audit of the best segmented candidate, and the direction for Round 8 (a controllable curvature-concentration family).

Interpretation · Interpretation

A comparison of two reliable higher-order controls and a tentative working proposition, stated as applying only to this round's research family.

Search-Control Audit

Explains why the heuristic search result for the m=2 segment family cannot be taken directly as evidence of that family's mathematical disadvantage — it is under-search, not a curvature effect.

Files · Files

sha256 61b02f8d8864a5b8cfb183e1c14203e57e360816d602cfb3b3ebbaba321f41ec