Pole Theory: A Discrete Scalar Framework for the Origin, Evolution, and Geometry of the Universe – Unifying Quantum Mechanics and General Relativity (Maximized Version)

This work presents a maximized formulation of Pole Theory, a discrete scalar field framework unifying quantum mechanics, general relativity, and cosmology. The universe is modeled as emerging from a state of absolute zero—defined not as physical emptiness but as a pre-geometric null state in which pole–antipole pairs exist in Grassmann-type superposition, satisfying antisymmetric relations such as θ₍ᵢⱼ₎ = −θ₍ⱼᵢ₎ and θ² = 0. At a critical pole density, internal symmetry collapses, initiating the Big Bang as a curvature-pressure singularity. Time and space emerge through asymmetric field evolution governed by a scalar polar field φ(x, t), defined as the product of two components: T(x, t) (polar tension) and Kₜₕₑₜₐ(x, t) (curvature phase). Thus, φ(x, t) = T(x, t) × Kₜₕₑₜₐ(x, t). From this, a unified scalar field equation is derived of the form:   □φ + m²φ + λφ⁴ = (8πG / c⁴) × (T^φ / φ) × R Where □ is the d’Alembert operator, m is the effective mass term arising from field locking, λ is the self-interaction coefficient of the polar field, and R is the Ricci curvature scalar. This equation embeds the structure of quantum fields, gravitational dynamics, and cosmological inflation within a discrete geometric context. Energy, mass, charge, and spin emerge as collective properties of pole density, symmetry, and locking configuration. Reduction of the polar field under symmetry constraints leads naturally to the Dirac equation, the Fermi Lagrangian, and SU(1) × SU(2) × SU(3) gauge representations. Gravitational phenomena—including black hole curvature, evaporation, and wave propagation—are modeled as macroscopic oscillations and collapses of the polar field. The cosmological constant Λ arises dynamically as the initial imbalance of superposed pole symmetry, expressible as Λ ≈ ∂²φ / ∂t² ÷ φ evaluated near the Big Bang. The theory predicts observable gravitational wave echoes, pole-field-dependent deviations in collider experiments, and anisotropic field memory in the cosmic microwave background. Falsifiability is achievable at both Planck-scale energy thresholds and astrophysical scales through structured phase interference. This paper refines and expands upon the original pole theory framework, incorporating pre-Big Bang geometry, quantum emergence, Hamiltonian formulation, decoherence, and the eventual return to zero via symmetry relaxation. It concludes with philosophical reflections on duality, causality, and the encoding of universal memory within the polar curvature field.