Rademacher's Half-Ball and Cone Counterexample in Three Dimensions

Rademacher proposed a half-ball joined to a cone, with a small tip truncation, as a counterexample to monotonicity of the expected volume of a random tetrahedron under inclusion. We prove that this specific construction works in dimension three, with cone height 10^-5 and truncation height 10^-10. A plane-section reduction and a finite lower Darboux sum, evaluated with integer-only outward interval arithmetic, certify that the half-ball expectation exceeds its origin-anchored counterpart 9*pi/1024 by more than 1/6000. A quantitative mixture argument transfers the gap to explicit nested convex bodies. The source archive includes the certificate program, all row sums and supplementary replays. General three-dimensional nonmonotonicity was already proved by Kunis, Reichenwallner and Reitzner using a tetrahedron; this preprint verifies the specific half-ball construction. It is computer-assisted, self-audited and unrefereed, without an absolute priority claim or a claim of formal verification. AI-assisted tools supported research, computation, proof development and manuscript preparation. The author is responsible for the final text. Corpus identifier: OWR-4136-005.