nx_curviness_gate.nx

nx_curviness_gate.nx -- GATE for aesthetictwin rung AT2 (outline curviness), the measure the published evidence prefers to the waist-to-hip ratio. THE DONE-RULE THIS GATE ANSWERS WAS WRITTEN INTO aesthetictwin.plan BEFORE ANY CODE, and it asks for exactly three things: that the metric ORDERS two silhouettes of equal waist-to-hip ratio and different curviness, that it is INVARIANT UNDER UNIFORM SCALE, and that a straight-sided silhouette reads zero. T4, T5 and T6 are those three. They are not paraphrased here from the implementation -- the implementation was corrected to meet them, because a first draft returned a per-row density that RISES when a body is merely smaller, and the pre-declared invariance requirement is what caught it. THE LOAD-BEARING TOOTH IS T4 AND T3 IS WHAT MAKES IT LOAD-BEARING. The gentle and sharp bodies are built with the SAME height, the SAME waist and the SAME hip -- so an identical waist-to-hip ratio, which T3 proves by measuring it with this organ's own narrowest and widest primitives. They differ only in WHERE the taper happens: the gentle body sweeps from hip to waist over its whole height, the sharp body pinches in over the middle half and runs straight above and below. A measure that is a ratio in disguise CANNOT separate them, because every input a ratio reads is identical. EVERY FIXTURE IS ASSEMBLED AT RUNTIME AND IN MEMORY, so this gate can never share a fixture with a production beat, and the widths are painted as an EXACT left-aligned run so the measured run length IS the width with no centring round-off. That is not cosmetic: the signal here is a total second difference of order 8 slope-units, and a plus-or-minus-one quantisation per row would swamp it.