Harmonic Convergence Theory: Mathematical Appendix
\Psi(r, t) = A(r) \cdot \cos(\omega_0 t + \phi(r))
:
God Frequency — the fundamental oscillatory mode originating from the Big Bang.
: Spatially varying phase function due to medium interference patterns.
: Local amplitude modulated by constructive/destructive interference.
This wave function represents a cosmic standing wave field permeating the interstellar medium.
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II. Boundary Conditions and Quantized Resonance
We define natural harmonic standing wave modes via:
\lambda = \frac{2\pi R}{n}
:
Allowed wavelength
: Effective boundary radius (resonance domain)
: Mode number (harmonic quantization)
The corresponding frequency is:
\omega_n = \frac{2\pi v}{\lambda} = \frac{n v}{R}
Where is the propagation speed in the medium (possibly ). These quantized modes manifest as particle-like stability — a proposed root of observed mass.
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III. Phase Divergence and Spatial Expansion
Define the spatial expansion field :
\mathfrak{E}(r, t) = \frac{\partial \phi(r)}{\partial r} \cdot \frac{\partial a(t)}{\partial t}
:
Phase decoherence gradient
: Rate of scale factor change
Interpretation: As wavefronts diverge in phase over distance and time, this mimics “space expanding.”
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IV. Rewriting Einstein’s Field Equations
Standard form:
G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
HCT Replacement:
G_{\mu\nu} + \mathfrak{E}(r, t) \cdot g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
Here, dynamically replaces , grounding expansion in wave interference rather than vacuum energy.
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V. Redshift Reinterpretation
Traditional redshift:
1 + z = \frac{a(t_{\text{obs}})}{a(t_{\text{emit}})}
In HCT:
1 + z = \frac{\omega_0}{\omega_0 - \Delta\phi(r, t)}
Where is the accumulated phase shift over travel distance. This proposes that redshift is not space stretching, but a product of phase diffusion.
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VI. Gravitational Attraction via Interference Nodes
Stable interference zones (nodes) correspond to gravitational attractors:
Energy density increases where standing waves constructively interfere
These zones create curvature-like effects by guiding neighboring wavefronts
This implies gravity is not a force but an emergent behavior of convergent resonance patterns in the wave field.
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More derivations to follow in upcoming sections: charge emergence, orbital quantization, biological coherence, and more.
End of Appendix v1.0
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