We establish, within the framework of Holographic Vacuum Elasticity (HVE), that the effective vacuum action of any confined quantum system with continuous isotropic symmetry undergoes a deterministic, topology-forced dimensional reduction. Applying Morse Theory to the bounded phase space, we prove that the phase manifold is diffeomorphic to the closed D-dimensional ball BD. Gauge invariance then enforces transversality via the Ward–Takahashi identity, constraining the vacuum action to be an exact differential form. The Generalised Stokes Theorem collapses the bulk integral identically onto the (D−1) -dimensional hyperspherical boundary SD−1, whose Haar measure is the solid angle ΩD−1 = 2πD/2/Γ (D/2). The resulting dimensional selection rule n = D − 1 is therefore a rigid topological invariant, not a phenomenological fitting parameter. Building on this geometric foundation, we present the Universal Vacuum Suppression Law (VSL): Oobs = Oideal · exp (−χσ0GWΩD−1fG), where χ ∈ +1, 0, −1 encodes suppression, invariance, or amplification; σ0G = αG (ΛG) /2 is the gauge coupling at the sector scale; W is the topological maturity index (W = 1 in flat vacuum) ; fG = 1/ (dim Rmed) 2 is the Schur–Reynolds fraction; and Oideal = C2 (V) × ΛG is computed from the quadratic Casimir eigenvalue and transmutation scale with no reference to the measured value. All primary theorems have been formally verified in Lean 4 with the Mathlib 4 library; every principal theorem carries zero undeclared axioms and zero sorry placeholders. A single infrastructure gap—the Hausdorff measure of SD−1 pending Mathlib coarea formalisation—is epistemically isolated. Quantitative predictions in hadronic, baryonic, and molecular sectors are presented with three falsifiable experimental tests.
Luís Cézar Rodrigues (Fri,) studied this question.