Persistence Without Contradiction: A Minimal Foundation for Existence

This paper establishes that persistence without globally coupled contradiction is structurally non-negotiable—the bedrock constraint on determinate existence itself.

Any entity that persists as identifiable must satisfy two independent conditions:

(1) Recursive closure: maintenance of stable identity under re-application of its defining boundary operation; and

(2) Energetic viability: maintenance of its boundary without exceeding available sustaining capacity.

These are not philosophical preferences but eliminative constraints. Forms that violate either condition cannot persist by structural necessity.

The argument proceeds through formal proof:

∙ The constraint applies to itself, grounding without regress (Theorem 29)

∙ Any evaluable denial presupposes the constraint it attempts to reject (performative closure)

∙ No more primitive alternative foundation exists (Propositions 32–38, exhaustive elimination)

∙ Classical paradoxes (Liar, Russell, Sorites, Ship of Theseus, Grandfather) resolve through uniform structural diagnosis (Section 10.5)

∙ The framework is falsifiable via an explicit three-way exhaustive trilemma (Section 9.4)

The constraint precedes physics, mathematics, and logic as usually formulated. It is not a theory about reality, but the filter reality must pass to exist as determinate form. Persistence is not a property added to systems; it is the structural precondition that determines which systems can exist as systems at all.

Key results include:

∙ Formal proof that recursive closure and energetic viability are logically independent (Theorem 27)

∙ Demonstration that globally coupled contradictions eliminate re-identifiability by structural necessity, not logical explosion (Theorem 25)

∙ Proof that CRIS architecture (Consistency, Recursion, Invariance, Selection) emerges as necessary consequence (Proposition 46)

∙ Closure of the use-mention gap for existential claims (Theorem 4)

∙ Operational collapse theorem for existence predicates (Theorem 42)

Domains of application. The constraint applies universally: mathematics (determinate structures), physics (conservation and observables), computation (stable state machines), formal systems (non-trivial inference), language (reference), and any domain requiring re-identification under transformation.

Relation to companion work. This paper provides the philosophical foundation and eliminative grounding for the CRIS framework.