The Self-Validating World: An Empirical Continuum of Cumulative Complexity Across Substrate Rings

We propose that the world is best understood as a self-validating system of models, in which functional structures (F) — abstract specifications of inputs, outputs, and transformations — realised in substrates (S) mutually validate one another through a binary selection operator Σ (a binary reformulation we propose; see §2.1) acting via cycle closure. The cycle-closure mechanism is the one developed in autocatalytic set theory (Kauffman 1971) and hypercycle theory (Eigen 1971), and rigorously formalised as RAF set theory by Hordijk and Steel (2004). Our contribution is to extend this mechanism from chemistry (its original domain) and economics (Koppl et al. 2022) to substrate rings spanning cosmic history, and to add a temporal element (carrier density ρ_S) that proposes to explain observed acceleration across substrate transitions. The food set for each substrate ring above the root is matter structured by the models of the previous ring; the root ring of fundamental physics uses protomatter — finite raw material of the universe in a pre-validation state — as its food set.

We test the framework empirically against four substrate rings spanning 13.8 Gyr — cosmochemistry (elements), mineralogy (mineral structures), biology (protein folds), and cognition (validated knowledge) — and find that each ring closes faster and more recently than the one before: the doubling time of its growth phase shortens by orders of magnitude across the sequence (from ~Gyr for cosmochemistry to ~10² yr for cognition, which has not yet plateaued).

Two minimal simulations are reported: one confirms emergent saturation under the closure mechanism; one yields a negative result on naive densification, disciplining the temporal claim.

We develop the ontology in seven interlocking formulations (binary Σ via cycle closure, nested rings of validation, primitive root contingency, food-set / protomatter resolution, densification, elimination as validation, and structural information preservation) and identify three falsifiable predictions about contemporary substrate transitions.