Persistence Without Contradiction: A Minimal Foundation for Existence

This paper establishes that persistence without contradiction is structurally non-negotiable. The bedrock constraint on existence itself. Any entity that persists as identifiable must satisfy two independent conditions:(1) Recursive closure, the maintenance of stable identity under re-application of its defining operation; and(2) Energetic viability, the ability to maintain its boundary without exceeding available resources. These are not philosophical preferences but eliminative constraints: forms that violate either condition cannot persist by structural necessity. The argument is established through formal proof: The constraint applies to itself, grounding without regress Any denial presupposes the constraint it attempts to reject (performative paradox) No more primitive alternative foundation exists (exhaustive elimination) Classical paradoxes (Liar, Russell, Sorites) resolve through structural diagnosis The framework is falsifiable via an explicit and exhaustive trilemma 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. Persistence is not a property added to systems; it is the structural requirement that determines which systems can exist as systems at all. Key results include: A formal proof that recursive closure and energetic viability are logically independent Demonstration that globally coupled contradictions eliminate invariance by structural necessity rather than logical explosion Proof that CRIS architecture (Consistency, Recursion, Invariance, Selection) is a necessary consequence of persistence Domains of application. The constraint applies universally across mathematics (well-defined structures), physics (conservation and invariants), computation (stable states), formal logic (non-trivial systems), and any domain requiring re-identification across transformations. This work provides the philosophical foundation for the CRIS framework. The companion paper CRIS Canonical Form supplies the mathematical formalization and generative dynamics.