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Theory: Mathematical Background and Extension

Harmonic Coherence is presented as an extension layer over established relativistic structure. This page summarizes the baseline equations and then outlines where the model introduces additional assumptions.

Conceptual Interpretation

In the Harmonic Coherence formulation, phase relationships are treated as dynamically coupled across nested temporal layers. The working objective function favors entropy-limiting trajectories under bounded phase deviation assumptions.

Within this interpretation, gravity, quantum dynamics, and field interactions are modeled as regime-specific projections of a shared coherence structure rather than fully disjoint formalisms.

The Core Concept

The relativistic baseline can be summarized with two directional statements:

1. Matter tells space how to curve:

[Mass-Energy]→[Spacetime Curvature]\text{[Mass-Energy]} \rightarrow \text{[Spacetime Curvature]}

2. Space tells matter how to move:

[Curved Spacetime]→[Matter Motion]\text{[Curved Spacetime]} \rightarrow \text{[Matter Motion]}

Mathematical Framework

We can express these ideas mathematically using tensors. Let's build up to the full equation:

Step 1: The Einstein Tensor

Gμν=[Spacetime Curvature]G_{\mu\nu} = \text{[Spacetime Curvature]}

This tensor GμνG_{\mu\nu} represents the curvature of spacetime

Step 2: The Source

Tμν=[Mass-Energy Distribution]T_{\mu\nu} = \text{[Mass-Energy Distribution]}

The stress-energy tensor TμνT_{\mu\nu} describes the distribution of matter and energy

Step 3: The Connection

Gμν=8πGc4TμνG_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}

Einstein's field equations relate curvature to stress-energy.

The Complete Picture

Including the cosmological constant Λ\Lambda, the full equation becomes:

Gμν+Λgμν=8πGc4TμνG_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}

This equation defines the standard coupling between geometry and energy-momentum used throughout modern gravitation theory.

How Harmonic Coherence Extends This

Harmonic Coherence introduces an additional temporal-layer structure and proposes a coherence tensor coupling between geometric curvature and inter-layer phase relations. The framework is constructed to recover established equations in limiting regimes while generating testable deviations outside those limits. These claims remain subject to external review and experimental validation.