The Awakening of Geometry: From the Quantum "Patchwork Labyrinth" to Pure Orthogonal Field Geometry

For over a century, fundamental physics has relied on an empirical patchwork—from Schrödinger’s scalar omission to Pauli’s $2 \\times 2$ matrices and Dirac’s minimal coupling—to fit quantum anomalies into rigid Cartesian coordinates. This paper presents Pure Orthogonal Field Geometry, demonstrating that matter is trapped light within a self-consistent $90^\\circ$ orthogonal dual-disk ($2\\text{D}+2\\text{D}$) topology, resolving micro-physics without Higgs mechanisms or unobservable abstractions. Rest Mass Derivation ($\\Delta h \\approx 0.236$): Governed by dual-opposite spatial tension $s(x) = \\frac{1}{x^2} - x^2$ at potential curvature $U''(1) = 4$, rest mass ($511\\text{ keV}$) is derived directly as net localized strain $\\Delta h = \\sqrt{5} - 2 \\approx 0.236$, stretching geometric capacity to the golden reciprocity limit ($h(1/\\phi) = \\sqrt{5}$). Deconstruction of Charge ($|q|=1$ and $+/-$): Absolute charge magnitude ($|q|=1$) emerges as a uniform 3D scalar envelope from planar face scanning ($\\cos^2\\theta + \\sin^2\\theta \\equiv 1$). Charge polarity ($+/-$) is dictated by the vector circulation of the odd generator $g(x) = \\frac{1}{x} - x$. Chirality, Spin-1/2, and Unified Fields: Electric fields (Planar Face) and magnetic fields (Line Profile) represent perpendicular projections of a single geometric entity. Spin-1/2 is naturally restored within a single $360^\\circ$ spatial revolution—eliminating ad-hoc $720^\\circ$ spinor hacks—while continuous loop circulation enforces the topological impossibility of magnetic monopoles ($\\Phi_{\\text{line}} = \\oint \\mathbf{B} \\cdot d\\mathbf{A} = 0$).