A Constraint Theorem on Helical History

A Constraint Theorem on Helical History presents a minimal structural result concerning persistence under transformation. Within a non-teleological, non-metaphysical framework, the note proves that any persistent history exhibiting both identity recurrence and irreversible accumulation cannot be cyclic. Instead, such histories necessarily admit a helical (spiral) structure in admissible state space, characterized by recurrence in identity evaluation and monotone advancement in a non-invertible structural parameter. The result is independent of spacetime assumptions, physical dynamics, computational models, or representational choices. It functions at the level of structural necessity, restricting what forms of persistence are admissible rather than predicting outcomes or proposing mechanisms. A minimal realization bridge is stated, under which the constraint applies conditionally to physical systems, without asserting that any particular physical system satisfies the required conditions. Explicit falsification criteria are provided: the result fails if a persistent system can be shown to exhibit true cyclic recurrence with memory and no irreversible accumulation. This note is intended as a concise, citable constraint placement within the broader structural ontology developed in Recursion, Constraint, and Persistence (Canonical Release v1.0). It does not propose a physical theory, cosmological model, or metaphysical interpretation. Its contribution lies solely in the exclusion of cyclic histories under clearly stated structural conditions. The work is suitable for readers in foundational physics, philosophy of science, theoretical computer science, and related fields concerned with persistence, irreversibility, and structural constraints on history.