The Helical Imperative: A Structural Framework of the Universe

This paper proposes a structural framework for persistence: the conditions under which a distinct entity can maintain its boundary across time. Starting from a single axiom — that no system with finite energy can process the Infinite, and therefore existence requires bounds — the framework derives: (1) the helix as the minimal topology consistent with recurrence, displacement, and scale invariance under dissipation; (2) seven structural invariants that constitute the minimum persistence conditions for any bounded system; (3) a measurement-theoretic grounding showing that constitutional parity between probe and target produces irreducible aliasing at the Nyquist floor, with the Heisenberg uncertainty bound reframed as the aliasing floor at constitutional parity; (4) an epistemological diagnosis of the GR–QM incompatibility as a conflict between incompatible methods applied to the same self-referential measurement problem; (5) agency as a structural consequence of sufficient complexity rather than a teleological addition; and (6) consciousness as instantiation-dependent bounded self-measurement. The framework is grounded empirically by four independent astronomical scale domains spanning eighteen orders of magnitude in period, none designed to fit the framework. The Milankovitch obliquity cycle serves as an undesigned control group: its geometric projection factor sin²(obliquity) = 0.1582 appears as the Constitutional Parity master coupling constant without adjustment, in a physical system whose dynamics were fixed by solar-system gravitation 4.5 billion years before the theory. The mathematical foundation for the multi-scale structure is the Three-Gap Theorem (Sós 1957). All claims are explicitly classified by epistemic status. Open problems are named. Falsifiable predictions are specified. The framework is a companion to The Quiet Price of Endurance (doi: 10.5281/zenodo.18676416), which establishes the accounting framework from which the geometric consequences are derived here.