nx_uvunwrap_gate.nx

nx_uvunwrap_gate.nx -- the gate for nx_uvunwrap_lib (/compare/dcc DC5). THE HAZARD THIS GATE IS SHAPED AGAINST. A parameteriser is unusually easy to fake, because the two obvious ways to fail both score well on the obvious metrics: * MAP EVERY VERTEX TO ONE POINT and every triangle is a perfect similarity of nothing. Angle and area distortion computed over non-degenerate triangles are zero because there are no non-degenerate triangles left to average. The tooth that kills it is chart AREA, and it is planted and bitten here. * FOLD THE CHART OVER ITSELF and the per-triangle metrics stay small while the atlas is unusable. The tooth that kills that one is the flipped-triangle count, and the unseamed cylinder below is a real mesh that actually produces it rather than a synthetic case. So the load-bearing structure is: a POSITIVE CONTROL that must come back at essentially zero, a DISCRIMINATION pair that must come back different, and a planted defect for every refusal class. WHY A DEVELOPABLE SURFACE IS THE RIGHT POSITIVE CONTROL, AND WHY THIS IS A HARD CLAIM RATHER THAN A SOFT ONE. A surface with zero Gaussian curvature is EXACTLY parameterisable -- an isometry into the plane exists, so the true minimum of the conformal energy is zero and any distortion measured on one is a bug in the solver, not a property of the input. Three of the fixtures below are developable for three different reasons (a plane, six planes cut apart, a piecewise-flat prism wall with no interior vertex) and all three must read at or under the tolerance. WHY THE CURVED FIXTURE IS A PYRAMID AND NOT THE CYLINDER THE BRIEF SUGGESTED. A cylinder WALL is developable -- it unrolls with no distortion at all -- so a cylinder reading non-zero would be reporting its own TOPOLOGY (an uncut annulus cannot embed in the plane) rather than curvature, and reading that as a curvature measurement would be measuring a different subject than the one being named. The pyramid's apex is a genuine cone point: four faces meet there with a total angle of 282 degrees against the 360 a plane would need, a deficit of 78 degrees that no cutting can remove. It CANNOT be flattened, so its distortion must be non-zero, and this gate prints the number rather than asserting a bound it invented. The cylinder still appears -- in both states -- because it is the only fixture that proves a seam does anything: the same 16 triangles refuse as a fold uncut, and unwrap cleanly with one edge cut. COMPOSES nx_meshvalid_lib rather than carrying a second validity checker, per the brief and per the duplicate-ruler law. 100% sovereign. No hardware writes (Rule 26). license_tier: ORIGINAL expect_exit: 0