Daphne Garrido

September 21, 2026

Derivation of the Relational Bio-Seismograph Index (RBSI) from the URCL.pdf

The Relational Bio-Seismograph Index is the concrete biophysical expression of the Universal Relational-Geometric Coherence Law. It takes the abstract coherence variables of the URCL -- local coherence, geometric protection, and dissipative load -- and maps them onto four measurable, or at least conceptually measurable, physiological quantities.

This article records the mapping, shows why the critical threshold remains the golden ratio phi, and distinguishes the classical physiological ingredients from the novel geometric construction.

1. The Four Biophysical Observables

The RBSI is defined by the scalar:

RBSI = (C_h * S_m * G_p) / A_l.

The four factors are interpreted as follows:

• C_h -- Heart coherence. A normalised measure of the stability and order of the heart-rate variability, or HRV, spectrum. It is typically obtained from the power in the high-frequency band or from the coherence ratio used in heart-rhythm research. Higher values indicate a more ordered, sinusoidally modulated autonomic state.
• S_m -- Magnetic / interoceptive sensitivity. A composite term that stands for the organism's capacity to detect weak magnetic and internal bodily signals. In the present framework, it is linked to the radical-pair chemistry of cryptochrome and to the interoceptive pathways that terminate in the anterior insula and anterior cingulate cortex.
• G_p -- Geometric protection. The biophysical counterpart of the Fibonacci-modulated protection factor kappa_ij of the abstract theory. It quantifies the degree to which relational and environmental interactions are organised according to golden-ratio scaling and are therefore resistant to resonant dissipation.
• A_l -- Allostatic load. A standardised index of the cumulative physiological cost of chronic stress, including elevated cortisol, inflammatory markers, reduced HRV, and related effects. It functions as the principal dissipative denominator that degrades the signal-to-noise ratio of the other three terms.

2. Mapping onto Abstract Variables

The global coherence balance equation of the URCL reads, in discrete form:

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

The mapping proceeds through the following identifications: