The triple unity of life: closure, code and the topology of living form

Abstract

What is common to every living thing? This paper develops a framework — three universalities of unequal strength, closed into a regulatory loop — as a Lakatosian research programme with a declared hard core, a graded protective belt, and a ranked positive heuristic. Four new results carry the weight. (1) Monte-Carlo margin analysis: measured rotor/gradient pairs sit at a mean 12.5th percentile of a neutral null under four registered null models, so c-rings run close to the thermodynamic floor as a statistical fact, with the mammalian c8 rotor the tightest-constrained case. (2) An exhaustive design table of 9,936 three-node signed loop topologies: self-maintenance is generic, robustness is graded by sign class, the all-positive class is the most robust, and the canonical loop sits mid-class. (3) A basal-leak extension reconciles the exactly absorbing dead state with the design table: spontaneous ignition is rare (6.8% of parameter sets) and gated by a smooth critical-leak line, so genesis requires founder events; spatially, pinning is structural and vesicle-like dispersal unlocks invasion above a critical coupling. (4) The same loop, applied to a second ignition with independent historical constraints, accounts for eukaryogenesis: the prokaryotic genome ceiling, the non-transferability of membrane-buried genes, and the singularity and irreversibility of the event. Honest negatives are reported throughout. Eleven predictions with frozen protocols close the paper.

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