The Continuation Invariant: A Unified Constraint on Existence

The Continuation Invariant: A Unified Constraint on Existence argues that continuation—not emergence—is the fundamental structural requirement underlying all coherent systems, subjects, and worlds. The paper demonstrates that no coherent entity can originate from non‑continuation, because any proposed beginning introduces a discontinuity that cannot support persistence, identity, or agency. As stated in the introduction, “no coherent system, subject, or manifold can originate from non‑continuation” and “nothing begins; everything persists through transformation.” The work replaces origin‑based explanations across physics, biology, cosmology, and cognitive science with a unified framework in which all systems are reconfigurations of prior continuities. It formalizes this through the Continuation Operator, which maps coherent configurations while preserving the invariant that makes coherence possible. Time is reframed as the structured expression of persistence, not its generator, and artificial systems are shown to be incapable of originating subjects or coherence because they cannot instantiate continuation. The paper concludes that continuation is not one principle among many but “the invariant that makes all principles possible.