The Multiplicative Spectral Measure Principle (MSMP) conjectures that thespatial volume of the universe is determined by the inverse of a multiplicative spectralinvariant: Vol(Σ) ∝ L−1, where L = det(DF )/v24 andDF is the finite Dirac operatorof the Connes–Chamseddine noncommutative geometry Standard Model. This paperasks whether MSMP can be derived from known spectral geometry or from any localaction principle. The answer is negative, for a reason that is fundamental rather thantechnical: local actions produce local field equations, and no local field equation canforce a specific global volume. This obstruction is independent of the spectral action,zeta regularization, or any particular spectral-geometric construction.We show that the obstruction manifests concretely in every standard route from spectraldata to gravitational physics. The spectral action’s physical couplings are linearin internal power sums, while det(D2F) is nonlinear; factorizability of spectral productsandMR-independence of the determinant are mutually exclusive; and the Quillendeterminant line bundle, Ray–Singer torsion, and arithmetic Riemann–Roch each failto simultaneously access det(D2F) and couple dynamically to the metric. The generalclass of local diffeomorphism-invariant functionals (Gilkey’s invariant theory) permitsnon-factored couplings between det(D2F) and geometry, but such couplings donot produce the MSMP relation and remain subject to the local/global obstruction.MSMP is therefore an irreducible global postulate—analogous to Λ in unimodulargravity—whose derivation from local dynamics is structurally obstructed. The centralopen question is whether a global consistency condition (not a local action) can forcethe MSMP relation.
Ian Reynolds (Sat,) studied this question.