Persistence and Complexity: Necessary and Sufficient Conditions for Physical Persistence, with a Systems Architecture of Life, Complexity, and Cosmic Silence

Persistence and Complexity

The Persistence Theorem and Recursive Gradient Coupling are companion works addressing different questions. They are presented here together because neither is complete without the other.

The Persistence Theorem asks what any autonomous physical process must do to persist indefinitely. It derives three conditions from established physics: non-equilibrium statistical mechanics, Kramers stability theory, Landauer's principle, and branching process theory. The conditions are necessary and sufficient. A process that satisfies all three persists for as long as a gradient is available. A process that fails any one terminates in finite time.

The three conditions are:
(I) gradient coupling with structural surplus: the process must build organised structure faster than it loses it.
(II) active homeostasis: the process must maintain its own boundary conditions using energy from its own coupling operation, not from an external agent.
(III) loop closure: the output of the process must include the means to run the process again.

They describe a class of thermodynamic process. Life is the most familiar member of that class. The conditions apply wherever the physics applies.

Recursive Gradient Coupling takes those three conditions as its starting point and asks what a gradient-rich universe becomes when they operate across cosmic time. From that single question, the following are derived: a tier hierarchy in which each level accesses a qualitatively deeper class of free energy, accessible only once the level below has built sufficient structural stock; a formal transition threshold with a dual criterion requiring both structural stock and coordination maturity; the Michaelis-Menten and Holling Type II equations as special cases of the same derivation; the Gompertz-Makeham mortality law from the homeostatic integrity dynamics; and the darkening law, a strict theorem establishing that detectability decreases monotonically with structural depth. The apparent silence of the universe follows as a necessary consequence.

Four extensions apply the framework to: (1) a quantitative model of Earth's tier-three transition spike, calibrated against the atmospheric nuclear test record; (2) the Fermi paradox and SETI search strategy; (3) ageing, cancer, reproduction, variation, and evolution as consequences of the homeostatic dynamics rather than foundational assumptions; (4) the origin of life as a thermodynamic threshold, including the bootstrap problem at genesis and why Darwinian selection begins at the first division.

Both papers make specific, falsifiable predictions. Both are presented as first articulations, not finished theories.

10.5281/zenodo.19154670


Further speculative developments of this theory can be found under the following links. These works are speculative and not considered to be complete works, they should be treated as such:

https://doi.org/10.5281/zenodo.19744391 - The Golden Recursion: The Golden Ratio as the Fixed Point of Recursive Persistence Under Scale Invariance
https://doi.org/10.5281/zenodo.19709008 - The Entropic Field: Gravity, Thermodynamic Persistence, and the Dark Universe as Orientations of a Single Thermodynamic Field
https://doi.org/10.5281/zenodo.19744531 - Unforeseen Consequences: The Quantum Foundation of the Entropic Field, Derived from the Three Persistence Conditions Without Intention

NOTE - This preprint obsoletes Life+ 10.5281/zenodo.18890632

This paper is pending arXiv submission in nlin.AO (Adaptation and Self-Organizing Systems), with cross-listing to q-bio.OT and astro-ph.EP. If you are a qualified arXiv endorser for nlin.AO and are willing to endorse, please get in touch at jack.wilding.work@gmail.com.