The Geometric Origin of Rest Mass: Pure Orthogonal Field Topology, Scale Reciprocity, and the Golden Strain Lock (Δh ≈ 0.236)

Dispensing with rigid Cartesian coordinate bias, ad-hoc Higgs parameters, and abstract probabilistic wave packets, this paper establishes a pure geometric framework for the origin of rest mass and microscopic particle structure. Space is formulated not as a passive, empty stage, but as an active, self-balancing geometric continuum governed by dual-opposite tensions: s(x) = 1/x² - x². Order Parameter & Strain Capacity Factorization: By factorizing the space-scaling field into an odd polarity generator g(x) = 1/x - x and an even capacity function h(x) = 1/x + x, we demonstrate that h(x) serves as the localized relativistic Lorentz strain factor γ_geom = cosh(η). First-Principles Derivation of Rest Mass: We show that an electron (511 keV) is a single gamma photon topologically trapped within a 90° orthogonal dual-disk (2D+2D) potential well locked at spatial curvature U''(1) = 4. As space transitions from the flat vacuum baseline (h(1) = 2) to the dual scale reciprocity boundary (x = 1/φ, where h(1/φ) = √5), space incurs a net localized binding strain of Δh = √5 - 2 ≈ 0.236. This net strain value directly defines the geometric origin of electron rest mass. Emergent 3D Spherical Envelope & Monopole Impossibility: The 90° orthogonal light circulation satisfies the scalar identity cos²θ + sin²θ ≡ 1, dynamically generating a perfectly homogeneous 3D spherical envelope (explaining null EEDM measurements). Electric fields (planar faces) and magnetic fields (line profiles) are unified as perpendicular geometric projections of one identical topological object, providing a definitive proof for the absolute geometric impossibility of magnetic monopoles. Physical reality rests upon an invariant triad: pure space geometry, lightspeed c, and Planck action h. Mass-energy equivalence (E = mc²) is demystified as the topological unlocking and stress release of cosmic geometric strain.