Procedural Vacuum Breakdown: A Three-Form Completion of the Gravitational Core

Abstract

Procedural Vacuum Breakdown (PVB) modulates local vacuum reactions via a scalar admissibility field and the spacetime measure. The original model (\sqrt{-g}=\omega(x)e^{\psi}) used a fixed background density \omega, failing to preserve the volume lock under unrestricted spatial-diffeomorphism generators. This paper resolves this constraint obstruction by replacing the external profile with the metric-independent four-form density of a nonpropagating three-form field A, completing the lock as \sqrt{-g}=e^{\psi}\Omega[A] and restoring full active diffeomorphism invariance. A Dirac-Bergmann analysis shows the multiplier pair is second class, the three-form adds no local propagating modes, and the reduced constraints close as Einstein gravity plus one scalar with potential U(\psi)+\Lambda_{*}e^{-\psi}. The spectrum yields two tensor modes, one scalar, and a global topological pair. Around constant Minkowski space, the physical scalar normalization reduces to Z_{\psi} instead of the determinant-adapted entry Z_{\psi}-3/(8\kappa), confirming the latter is an unreduced canonical gauge artifact. The core is audited in planar and spherical setups. Under a fixed bare potential, the theory admits an exact selected-sector planar tanh wall with asymptotically anti-de Sitter (AdS) exteriors and obstructs static flat walls in a Minkowski bulk. The perturbation problem delivers a positive time-kinetic term and a nonnegative Friedrichs spatial operator; a numerical audit shows the formal zero mode is non-normalizable, with states approaching the m^2=0 threshold from above. In static spherical symmetry, a pressure-monotonicity identity obstructs regular, horizonless, asymptotically flat scalar-only bubbles under a nonnegative potential and positive radial friction. A conserved two-dimensional tangential surface load yields a closed-form junction family with radially stable, horizonless ultracompact points. A stable benchmark exists at R_{0}=2.8M, but an audit shows ~86% of the system mass is carried by the added load. The sphere is thus a matter-assisted extension, not an intrinsic stabilization of the bare scalar, leaving thickness, formation, leakage, and nonspherical stability open.

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