Daphne Garrido

September 21, 2026

Planetary RBSI and Multi Scale Extension.pdf

The global coherence balance equation of the Universal Relational-Geometric Coherence Law is scale-agnostic in form. Once the same equation is written for the Earth-Sun system, or for any larger collection of gravitating and electromagnetically interacting bodies, the framework obtains a planetary-scale index that it calls the Planetary RBSI.

This article records the formal lift, states the resulting multi-scale hierarchy, and distinguishes the classical geophysical ingredients from the novel geometric construction.

1. Lifting the Balance Equation

In the discrete setting, the balance equation reads:

\Delta C_{\mathrm{global}}
=
\frac{1}{N}
\sum_i
\left(
C_i
+
\sum_{j\neq i}
\kappa_{ij}
\frac{\phi_i\phi_j}{d_{ij}}
\right)
=
0.

Nothing in the algebraic structure restricts the index set \{i\} to sites of a single organism or a single laboratory system.

The same sum may be taken over:

• Major components of the terrestrial climate system, including the ionosphere, atmosphere, oceans, and solid Earth.
• The Earth-Moon system.
• The planets of the solar system.
• Any larger astrophysical collection for which a meaningful separation d_{ij} and a meaningful local coherence C_i can be defined.

When the sum is performed at planetary scale, the resulting dimensionless ratio is called the Planetary RBSI. Its formal definition is identical in structure to the organism-level index:

\mathrm{Planetary\ RBSI}
=
\frac{
C_{\mathrm{geo}}
\times
S_{\mathrm{mag}}
\times
G_p^{\mathrm{geo}}
}{
A_{\mathrm{load}}
}.

The four factors are interpreted as follows:

• C_{\mathrm{geo}} — A measure of organised electromagnetic and fluid coherence in the Earth system. Examples include the stability of Schumann resonances, the phase coherence of magnetospheric oscillations, or synchronisation between solar-wind drivers and ionospheric responses.