A paper called the General Theory of Relational Primacy (GTRP) argues that complex systems are best understood by the relations between their parts, not by the individual variables we usually measure. The authors claim that crises begin when these relations quietly reorganize, and that watching those relational changes gives earlier warning than watching the variables themselves. They propose a concrete way to measure those relational shifts and report tests on climate data and simulations that support the idea.

The researchers set out three axioms that form the foundation of their theory. The axioms say that relations are primary, that relational change comes before visible changes in variables, and that every observation involves some coupling between variables that can be measured. From these axioms they build a formal framework with specific hypotheses (H1–H5), conditions for when the approach is valid (C1–C6), and properties of an observable they call β. They also state a general theorem that every complex system contains an irreducible relational level, introduce an invariant similar in spirit to conservation laws, and give definitions for crisis and relational causality.

The key observable is the parameter β(t) = d log y / d log x. In plain terms, β is the elasticity between two variables: how a percentage change in x relates to a percentage change in y. The authors estimate β over time using a time-varying Kalman filter, a statistical method that tracks changing parameters from noisy data. Working in log-log space makes β a measure of the coupling strength between variables. Mathematically, they argue that relational changes affect β with a sensitivity proportional to the size of the underlying change (written O(δθ)), while classical signals based on variables change only with the square of that size (O((δθ)²). This, they say, makes β able to detect reorganizations earlier.