Triadic Potential Field Theory (TPFT): Emergent Geometry from Ternary Data Synchronization

Abstract

The irreconcilability of General Relativity and Quantum Field Theory stems from the assumption of continuous spacetime and fundamental physical forces. This paper proposes the Triadic Potential Field Theory (TPFT), a framework that redefines physical reality as an emergent property of a localized, ternary data processing system. By postulating a fundamental informational triad (φ_-1, φ₀, φ₁) governed by a strict local balancing constraint (i+j+k=0), we present formal mathematical derivations bridging discrete ternary logic to continuum field theories. We demonstrate that SU(3) gauge symmetry is the exact transformation group preserving the local trace-zero constraint, while U(1) electrodynamics emerges from the necessity of local phase synchronization in the φ₀ network. Furthermore, by defining informational distance via the Fisher Information Metric, we derive the emergent thermodynamic geometry of spacetime and provide a novel interpretation of cosmological singularities, fermionic exclusion, and the fine structure constant (α).