# Verification report

The all-dimensional proof integrates the hinge function (d-s)_+ on a thin simplex. It includes every Euclidean boundary face and its correct area Jacobian. Taking the thickness h=d^2 and then d to zero gives a ratio tending to n. Larson's known upper bound gives equality of the universal constant. Smooth, positive, strictly convex approximation is performed on each fixed domain before the geometric limit.

The checker passes 4,072 exact arithmetic conditions in both normal and optimized Python, with identical complete reports. It uses generic determinant-based triangulations of clipped prisms, affine-function vertex averages and Gram-determinant face areas, independently of the written slicing calculation. The checks cover 135 parameter cases in dimensions 2 through 10, including the planar edge case, quantitative gaps, hinge convexity and exact quadratic-root sign controls.

All four final PDF pages were individually inspected. Equations, author footnote, scope qualifications, references and page transitions are legible without clipping or overlap. The built-in compiler reports success; the exported PDF log contains no errors, unresolved references, missing glyphs, overfull or underfull boxes. The package manifest binds the source, PDF, portable checker and expected reports.

The theorem is accepted by originating-model detailed self-audit. Finite testing and PDF compilation are not formal mathematical certification. No independent review or absolute priority is claimed. The boundary-mean convex subproblem is distinguished throughout from the remaining volume-power normalized questions.