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The closed-box certificate took exactly twelve triangles, two a face. The one mesher puts interior points on planar faces (a 20 x 20 x 2 box comes in more than twelve), so render.preflight refused a box as "unsupported dielectric boundary tessellation"; a box is a box however its faces are triangulated. The certificate now reads the mesh's geometry exactly: every triangle in the plane of one of the faces of the box its points span (corners on it, normal exactly that axis) facing out, and the triangles a closed, consistently oriented surface (each edge, by its ends' exact coordinates, run once each way). Such a surface is a 2-cycle on the box's boundary, a sphere, so it covers every point of it the same k >= 1 times, and its area is k times the boundary's: k = 1 is decided by the area being under 1.5 times the boundary's. Up to 65536 triangles. A thin sheet is still one or two triangles; a general closed mesh is still refused. New test: a box with its top fanned from a point in it is certified, with the same bounds; the point 1e-9 off the plane, or the top covered twice, is refused. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>