nx_meshcheck_gate.nx

nx_meshcheck_gate.nx -- proves the mesh integrity sweep, in BOTH directions, per defect class. THE POSITIVE CONTROL IS A TETRAHEDRON, and it is chosen because it is the smallest object for which every property under test is simultaneously non-trivial: 4 vertices, 4 faces, 6 edges each shared by exactly two faces traversing it in OPPOSITE directions, no loose vertices, no degeneracies, and an Euler characteristic of exactly 2. A cube would work too and would hide a winding bug behind more symmetry; a single triangle would pass most teeth vacuously because it has no shared edge at all. EVERY DEFECT CLASS GETS ITS OWN PLANTED MUTANT, because the classes have DIFFERENT REMEDIES and a detector that fires on all of them identically is one counter wearing six names. Each mutant is built at runtime from the same clean tetrahedron, so a tooth that fires is firing on exactly one injected difference.