Purpose vs Randomness

An M. Rodriguez (ORCID), Alex Mercer, Elias Thorne

Preferred Frame Writing — January 2026

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One-Sentence Summary

We define the Acausal Purpose Invariant ($\mathcal{P}$), a scale-invariant metric that quantifies how strongly a structure resists the combinatorial entropy naturally associated with its size.

Summary

We introduce the Acausal Purpose Invariant ($\mathcal{P}$), a decibel-scale measure of how atypical a number’s prime ancestry is relative to a stochastic background. Empirical sweeps reveal a sharp probabilistic cutoff separating random structure from cost-paid persistence, reframing the detection of life, artifacts, and purpose as a problem of entropy suppression rather than intelligence.

Keywords

Keywords: Acausal Purpose, Purpose Index, SETI, Technosignatures, Signal Filtering, Entropy, Universal Constants, Persistence, Teleology, Biosignatures

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