Ontological Motion from Analytic Protection with Terminal Matching

This work introduces the Ontological Topology Jump Protocol, a structural framework in which effective displacement between configurations arises from analytic protection, rather than from force-driven motion or traversal of continuous Euclidean paths. The central result is that persistent, non-collapse evolution is realizable if and only if system dynamics admit a complex-analytic representation equipped with a continuation-invariant identity functional. Within this framework, physical evolution is represented as analytic continuation on a complex manifold, while observed spacetime trajectories appear only as projections of this higher-dimensional analytic structure. A protected invariant—referred to as an identity functional—is defined and characterized operationally by vanishing loop drift under analytic continuation avoiding singularities. When analytic protection holds and terminal matching conditions are satisfied, path dependence becomes a gauge-level artifact: intermediate continuation paths lose ontological significance, and physical identity is determined solely by analytic equivalence between endpoints. This structure permits effective re-identification between spatially separated configurations without requiring a unique continuous Euclidean trajectory, provided analytic protection and endpoint matching are maintained. The protocol may be interpreted as operating across three conceptual layers:(i) suppression of net analytic drift through local compensation mechanisms;(ii) controlled continuation around singular structures; and(iii) holomorphic correlation enforcing identity preservation between entrance and exit configurations. These layers are presented as interpretive consequences of the analytic framework rather than independent axioms. A concrete realization is provided using the Riemann zeta function. A nontrivial invariant constructed from the arguments of the zeta function and its derivative is shown numerically to satisfy loop invariance, endpoint stability under matched continuation, and strong suppression of interior variation along protected paths. Additional numerical experiments demonstrate quadratic scaling of protected path cost and conservative behavior of the associated analytic forces. Within this framework, apparent nonlocal or superluminal features arise as projection effects of analytically protected continuation, rather than as signal propagation or force-mediated transport. At the structural level considered here, the protocol does not require violations of causality or conservation laws. Instead, transport is reframed as an identity-consistency problem, governed by complex analysis and topology rather than by Euclidean traversal.