The Unified Master Equation: A Ward-Balanced Δ–Σ Vacuum with a Structurally Selected IR-Stable Fixed Point at α = 3/2

Le résumé fourni par la source

The Unified Master Equation (UME) is a pre-geometric research framework built from two opposing vacuum sectors, Δ (contractive) and Σ (expansive), organized through an O→Q→S architecture in which spacetime is not assumed at the fundamental level but emerges from an underlying pre-geometric sector. Within the minimal Ward-balanced realization, Ward-constrained renormalization-group flow and structural-stability analysis jointly select the non-trivial infrared-stable fixed point α* ≡ Δ/Σ = 3/2. The value 3/2 is therefore not introduced as an empirical fit but arises as the dynamically selected balance point of the framework. At this fixed point, Ward-invariant projection from the pre-geometric Q-sector to emergent spacetime yields equality of temporal and spatial kinetic coefficients, Z_t = Z_x, and hence a universal invariant light cone, with a universal limiting causal speed identified with the speed of light, c, and Lorentzian causal structure. The same projection converts underlying unitary dynamics into effective irreversible open-system dynamics of GKSL type, providing a statistical arrow of time. The resulting causal and temporal structures are compatible with, but do not independently derive, a four-dimensional block-universe interpretation. Beyond these core results, the present work develops a broader UME research program and explicitly distinguishes derived results from model-derived, model-dependent, proposed, and interpretative extensions. These include constructions addressing entanglement and nonlocal correlations, black-hole information preservation and singularity avoidance, cosmogenesis and late-time expansion, effective dark-sector phenomenology, gauge and interaction structure, precision observables, mass hierarchies, neutrino phenomenology, the strong-CP problem, gravitational-wave signatures, matter–antimatter asymmetry, and recurrent 3/2 scaling across several physical domains. Quantitative benchmarks and reproducibility calculations are provided where explicit constructions are available, while incomplete first-principles connections are identified as open problems rather than established consequences of the framework. A concrete Higgs-portal realization provides a directly testable phenomenological benchmark: a predominantly Δ-like scalar resonance near 0.9 TeV, correlated through mixing with the observed 125 GeV Higgs-like state, with benchmark mixing angle θ = 9.85° (sin²θ = 0.0292) and characteristic hh, ZZ, WW and tt̄ channels. Additional laboratory, cosmological, precision, and gravitational-wave tests are formulated throughout the work. UME is therefore presented not as a completed theory of all fundamental physics, but as a unified and falsifiable pre-geometric research program centered on the dynamically selected α* = 3/2 fixed point. Its central question is whether this common Δ–Σ structure can provide a mathematically robust origin for emergent spacetime, causal structure and temporal orientation while generating distinctive predictions that survive increasingly precise experimental and observational tests.

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