Daphne Garrido

September 21, 2026

Global Coherence Balance Equation.pdf

The Universal Relational-Geometric Coherence Law is expressed most compactly by a single global constraint: the net change in coherence across an entire system must vanish.

This article states that constraint, explains the accompanying continuity, or flow, condition, and situates both objects relative to classical conservation laws.

1. The Balance Equation

For a finite collection of N interacting sites, the URCL postulates:

Delta C_global = (1 / N) * sum from i = 1 to N of [C_i + sum over j not equal to i of kappa_ij (phi_i phi_j / d_ij)] = 0.

Here:

• C_i is the local coherence, or local budget, associated with site i.
• kappa_ij is the pairwise geometric protection factor constructed from Fibonacci weights.
• phi_i and phi_j are local coherence amplitudes.
• d_ij is a positive separation measure between the sites.

The equation asserts that the average, over all sites, of the sum of each site's intrinsic coherence and its protected interactions with every other site is identically zero.

In other words, any local excess of coherence must be exactly compensated by a corresponding deficit elsewhere, once geometric protection is taken into account.

When the system is continuum rather than discrete, the same idea is written as a local continuity equation for a coherence current F_coherence:

div(F_coherence) = 0.

This is the statement that coherence is neither created nor destroyed inside any volume. It can only flow from one region to another.