Oscillation‑Phase‑Tilt and Spiral Wave Geometry - Formalization Papers

This submission is supplemental to the original set of papers published in Zenodo on 1/15/26 - Oscillation‑Phase‑Tilt and Spiral Wave Geometry: A Unified Minimal‑Principle Framework for Physics The OPT/SWG Framework derives the core structures of reality from a single invariant oscillation. These foundational papers—the Unified Formalization and the Companion Paper—bridge a more developed mathematical derivation with physical ontology, attempting to demonstrate that relativistic and quantum may be emergent consequences of an underlying oscillatory geometry. The Companion Paper: Reconstructing Physics from Oscillatory Geometry This paper provides a conceptual re-foundation of physics by grounding abstract constructs in a concrete geometric ontology. Using a single oscillation and a tilt identity, it derives relativity and quantum theory as necessary geometric consequences. Paradoxes like the invariance of light speed are dissolved by replacing symbolic machinery with null phase sheets (unwrapped modes) and matter (wrapped modes). The paper proves that quantum discreteness and relativistic transformations arise naturally from geometric phase closure. By explaining the physical "why" behind standard equations, it establishes a coherent ontology where mass, time, and motion are different projections of a single oscillatory process. The OPT/SWG Unified Formalization The Unified Formalization establishes the framework’s mathematical architecture, deriving field equations and an emergent metric from a primordial phase field. This explains macro-scale gravitational and cosmological phenomena without dark matter or dark energy. By formalizing the Phase-Tilt Connection, it ensures the framework is self-consistent and predictive across all scales. At the micro-scale, the paper illustrates how deterministic phase dynamics generate the probabilistic nature of quantum mechanics. It provides first-principles derivations of the Schrödinger and Dirac equations directly from the phase-field Lagrangian. Advancing the OPT/SWG Framework These papers transition the framework into a more mathematically robust research suite. By providing both more developed field equations and a clear physical ontology, they offer a self-contained reference for a minimal‑assumption derivation of physical law. This dual approach helps the framework reproduce modern physics' success while revealing the geometric origin of all phenomena.