Function shell_vector_areas 

pub fn shell_vector_areas(solid: &BrepSolid) -> VectorAreaReport

Does a closed shell’s boundary enclose the vector area it should — zero?

A patch’s vector area is a BOUNDARY integral, ∫_F n dA = (1/2) ∮_{∂F} r × dr, so the whole shell’s is a sum over the faces’ loops. Every edge of a closed shell is walked exactly twice, once each way, so Σ_faces ∫ n dA is exactly zero on a closed shell — a statement about the RECORD, with no tolerance in it, as long as the two faces meeting at an edge walk the same curve. They do not: each walks its OWN TRIM, the pcurve mapped through its own surface, and what is left over is the sum of every trim’s departure from the edge it claims.

That residual is the one whole-shell number that reads the trims — which is what every mass property is actually an integral over (geometry/pcurve.rs, PCURVE_REFINEMENT_TOLERANCE) — and nothing in the kernel read it before 2026-09-16. validate() compares a pcurve to its edge at pcurve_consistency (4e-3 on a small model, 2.5% of the diagonal on a large one): three defects on the notched cap sat between 5e-7 and 1.9e-5, four orders inside that bar, and the solid’s volume matched its closed form because two of them cancelled.

The bar, and where it comes from

Write a trim as its edge plus a departure, r = e + d. Over a CLOSED loop,

(1/2)∮ r×dr − (1/2)∮ e×de = (1/2)∮ (e×dd + d×de) + (1/2)∮ d×dd
                          = ∮ d×de + (1/2)∮ d×dd

(the middle step is one integration by parts: ∮ e×dd = −∮ de×d because the loop closes). So a face whose every trim lies within δ of its edge departs by at most δ · L, its own boundary length, and the second-order term is δ²-small. Summing over a closed shell, whose faces walk every edge twice, the strict bound is 2δ · Σ|e|.

δ is [PCURVE_REFINEMENT_TOLERANCE], 1e-7 — the 3D distance fit_pcurve_on_surface refines a trim to, and the floor under every mass property. The bar this module applies is the TIGHTER δ · Σ|e| — half the strict bound — because the worst case it drops is a shell where every pair of trims sits at the floor on OPPOSITE sides of every edge all the way round. A shell between the two is named, and the per-face bar says which faces put it there.

Two things the bar does not cover, both reported rather than absorbed:

• a fit that exited at crate::PcurveFitExit::SampleCeiling never reached the floor, so a shell carrying one can be over the bar and still be the best this kernel builds. That is a finding about the fit, not a reason to widen the bar.
• the quadrature’s own error, reported per shell as ShellVectorArea::quadrature_error. A residual inside its own error bar is not a measurement.

What it does not ask

It does not ask whether a face’s trim is in the right PLACE — a trim displaced along its own edge, or two faces’ trims displaced the same way, cancel in this sum exactly as they cancel in the volume. It is a closure test, not a fit test: d enters only through ∮ d×de. And it says nothing about an open shell, where the residual is the boundary’s own vector area and not a defect.