Published June 2, 2026 | Version v3
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Oscillation‑Phase‑Tilt and Spiral Wave Geometry - Formalization Papers

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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.

Abstract (English)

A Phase‑Geometric Origin of Annihilation: Wrapped Modes, Null‑Phase Photons, and the Compton‑Scale Radius in OPT/SWG

This paper develops a deterministic, geometric account of matter–antimatter annihilation within the OPT/SWG framework, where particles are finite‑energy “wrapped modes” of a single phase field and photons are null‑phase sheets released during topological unwinding. By deriving the wrapped‑mode radius from the balance of gradient, curvature, and internal‑oscillation energies, the work shows that the only possible micro‑scale is the Compton wavelength, not the Planck length. This establishes a concrete physical size for particle structure, links annihilation cross‑sections directly to R∼ℏ/(mc), and provides a unified geometric mechanism connecting winding cancellation, photon emission, and experimentally accessible Compton‑scale phenomena.

Internal and External Phase Advance: A Unified Phase‑Geometric Origin of Mass, Momentum, and Proper Time

This paper advances the OPT/SWG framework by showing that mass, momentum, proper time, and null propagation all arise from how a wrapped or unwrapped mode allocates the phase‑advance of the underlying oscillation. It extends earlier OPT work by demonstrating that the relativistic energy–momentum relation is not a postulate but a geometric identity linking internal and external phase components, and that time dilation, rest energy, and null behavior follow directly from this single phase‑budget mechanism. This supplement deepens the theory by revealing massless and massive modes as complementary phase‑allocation regimes of the same oscillatory process.

Compton-Scale Particle Dimensions in OPT/SWG

This paper develops an Oscillation–Phase–Tilt (OPT) and Spiral Wave Geometry (SWG) interpretation of elementary particle size. It proposes two complementary dimensions: a broad phase-envelope radius, associated with wrapped standing-wave closure, and a smaller interaction/contact radius, associated with collisions, scattering, annihilation, or phase-field overlap. Its central claim is that the reduced Compton wavelength, (\hbar/(mc)), naturally acts as the radius-like closure scale for a massive particle, while the full Compton wavelength represents the complete phase-cycle scale.
This interpretation offers a way to discuss particle size without conflicting with accelerator evidence that particles behave point-like at very short scattering distances. Collider experiments may chiefly constrain the hard interaction/contact scale, while a larger coherent phase envelope could still exist. The paper therefore proposes future work that distinguishes phase extent, interaction kernels, overlap thresholds, and compositeness limits, with possible implications for scattering data, annihilation behavior, and the relationship between mass, phase closure, and spatial scale.

 

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A_Phase_Geometric_Origin_of_Annihilation_v10-r2.pdf

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Is supplement to
Preprint: 10.5281/zenodo.18262511 (DOI)

Dates

Updated
2026-06-02
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