Bosonic Propagation as Phi-Toric Boundary Transitions: Toward a Unified Field Ontology in B.O.O.F. Cosmology

Abstract

The Big Boof Theory (B.O.O.F.) has progressively developed from a geometrically motivated cosmological proposal [Paper 1] through a rigorous mathematical formalization grounding the tuning force in the barycenter condition of toric Fano geometry and integrating Phi-toric tessellations into spinfoam loop quantum gravity [Paper 2]. The present paper completes a third layer of the framework by addressing the question left open in both prior works: what is the physical content propagating between Phi-toric vertices in the spinfoam? We propose that bosons — the force-carrying particles of the Standard Model — are not independent ontological primitives but are precisely the edge amplitudes of the Phi-toric spinfoam partition function Z_Phi: they are transitions between stable Phi-toric boundary states. Within this framework, each species of boson corresponds to a distinct class of Phi-toric boundary state transition characterized by the SU(2) representation content of the spinfoam edge. Spin-1 gauge bosons (photon, W, Z, gluons) correspond to edges carrying j=1 angular momentum between Phi-toric vertices; the spin-2 graviton corresponds to Phi-vertex-to-Phi-vertex transitions in which the degenerate geometry itself propagates; and, most significantly, the Higgs boson is identified as the scalar field whose vacuum expectation value enforces the global barycenter condition Bc(P_Phi) = 0 across the tessellated spacetime manifold. This last identification resolves a longstanding conceptual gap: the Higgs mechanism acquires geometric meaning as the physical stabilizer of Phi-toric resonance equilibrium. Together, these identifications unify the Standard Model force sector with the geometric stability framework of B.O.O.F., providing both conceptual coherence and a set of quantitative predictions distinguishable from standard quantum field theory.