nx_curve_smoothness_census.nx

nx_curve_smoothness_census.nx -- a WEIGHT-INVARIANT smoothness metric that actually isolates FACETING (the thing edge-complexity confounded). Insight: faceting is about the CONTOUR'S TURNING, not its thickness. A smooth curve turns UNIFORMLY (a circle's curvature is constant); a faceted polygon concentrates all its turning into a few sharp vertices. So along the traced outer contour: facet_index = n * Sum(T_i^2) / (Sum|T_i|)^2 where T_i = per-step turning of the tangent For a perfectly-uniform (smooth) contour this = 1.0; for turning concentrated at k corners it -> ~n/k. Scale-free, weight-free, trig-free (turning via integer cross-product of normalized tangent vectors). SELF-VALIDATING LIAR-KILL: a synthetic CIRCLE must read near 1 (smooth) and a HEXAGON must read MUCH higher (6 corners) -- if the metric can't tell a circle from a hexagon it declares ITSELF broken. Only then does it report our "O" vs Chrome's "O". license_tier: ORIGINAL expect_exit: 0