Closure Physics: The Physical Realization of the Seed Tetrad From Ontological Mathematics and Coherence Mathematics to Gauge-Gravity Unification

This paper develops Closure Physics as the physical realization of the ontological and mathematical foundations established in the preceding papers of the series. Paper 1 identified coherence as invariant ground and the five principal irreducibilities. Paper 2 derived the four minimal axiomatic requirements: relational continuity, complementary invariance and differentiation, mediation and transmissibility, and local reduction with reintegration. Paper 3 initiated coherence mathematics through the relational field, coherence functional, dual transformations, resonance mediators, and paired reduction/reintegration maps. The present paper shows how these formal structures are physically realized through dual bivector geometry, closure-cost functionals, and spectral decomposition. Central to this realization is the Seed Tetrad — 0⁰ = 1 (coherence from nullity), 0! = 1 (identity from absence), −e^(iπ) = 1 (phase/rotation/curvature closure), and ∞⁰ = 1 (scale-invariant unity) interpreted as a primitive disclosure architecture. These four seed equations map directly onto the four axiomatic requirements and provide the compact symbolic hinge through which ontological mathematics becomes physically operative. Closure Physics therefore reframes gauge interactions as discrete spectral attractors within a gravitational continuum, unifies gauge theory with gravity through closure functionals, and prepares the ground for cross-domain shell hierarchies. The framework does not replace standard physics but re-grounds it in the generative ontology of coherence, disclosure, and stabilized closure. The deeper foundations of ontological mathematics remain reserved for dedicated treatment; this paper focuses on the physical layer already compelled by the preceding ontological, axiomatic, and mathematical stages. Keywords: Closure Physics; Seed Tetrad; Ontological Mathematics; Unified Coherence Closure Framework; gauge-gravity unification; dual bivectors; closure functionals; spectral decomposition; disclosure; coherence mathematics