Viability of a Recursive Computation Substrate Under Full Noise: Structural Constraints for Noise-Robust Computation

This work presents a structural–empirical analysis of computation under sustained perturbation. Rather than treating computation as an operational or performance-defined process, the paper evaluates computation as a structural phenomenon grounded in identity preservation, admissible continuation, irreversibility, and constraint enforcement. The analysis is explicitly dependent on the foundational ontology developed in Recursion, Constraint, and Persistence, which derives recursion, admissibility, collapse, and irreversibility from the minimal requirement that identity must persist across transformation. No attempt is made here to justify that ontology independently; all conclusions in this work collapse if those foundations fail. Empiricism in this paper is defined structurally rather than physically. Claims are falsifiable with respect to inequalities, bounds, and necessity conditions over abstract state spaces, not through hardware benchmarks, physical noise models, or experimental measurement. The analysis is therefore implementation-invariant and avoids assumptions about speed, efficiency, optimization, intelligence, agency, or physical realization. We show that, under bounded adversarial noise, a recursively constrained substrate remains computationally viable if and only if five conditions hold:(1) identity tolerance exceeds noise magnitude,(2) admissible continuation exists,(3) structural entropy is bounded,(4) constraint violations induce structured collapse rather than undefined behavior, and(5) collapse preserves irreversible history and permits post-collapse continuation. The paper introduces a formal physical realization bridge, specifying necessary constraints that any physical system claiming noise-robust computation must satisfy, without asserting that any such system exists or that the framework derives physical law. An appendix demonstrates structural correspondence — not reduction — with quantum error correction, thermodynamic irreversibility, and classical fault-tolerant computation. This work does not propose a new physical theory, computational architecture, or algorithm. Its contribution is to identify minimal, falsifiable structural conditions under which computation can persist under noise, independent of implementation.