Substrate Computation and Phase Intelligence

A class of physical systems performs computation by instantiation rather than simulation their native dynamics are the operations we would otherwise simulate on general-purposesubstrates. A soap lm spanning a wire frame does not solve the minimal-surface problem; itarrives at the solution by being what surface tension makes it in the time it takes physics tosettle. A hydraulic valve body does not simulate state-machine logic; its machined geometryand force balance is the state machine. We call this class substrate computation.A subclass has a further property. The map from input to output is itself modiedby the history of operation, through slow physical variables of the substrate. This papergives ve operational criteria for that subclass, each with a measurement, a null model,and a signicance threshold. All ve must hold together on one system. We use phaseintelligence for the case in which the fast variables are oscillator phases, the slow variablesare physical couplings, and the ve criteria pass in a single experiment.The laboratory realisation is a lattice of radio-frequency oscillators whose couplings areanalog biases on reactive elements. After phase reduction and averaging, the coupling law is aphase-dierence-dependent plasticity rule implemented by a mixer and a leaky integrator not by an external optimiser descending a global cost. A two-year protocol at approximatelyUSD 225,000 tests the criteria on that closed analog system. The same rubric applies toany candidate medium whose state can be recorded. A companion paper (Part II) treatsdetection in natural continua. A companion paper, Detection Criteria for Natural Continua, is the second file in this record.