Δ𝓘 = 0: The Minimal Principle of Ontological Motion

This work introduces what we refer to as an Ontological Topology Jump Protocol—an interpretive framework in which effective displacement between configurations arises from analytically protected identity continuation, rather than from force-driven motion or traversal along continuous Euclidean paths. The central structural result is that persistent, non-collapse evolution is realizable at the ontological level only when system dynamics admit a complex-analytic representation equipped with a continuation-invariant identity functional. Within this framework, physical evolution is modeled as analytic continuation on a complex manifold, while observed spacetime trajectories arise solely as projections of this higher-dimensional analytic structure. A protected invariant—referred to as an identity functional—is defined operationally by vanishing loop drift under analytic continuation avoiding singularities. When analytic protection holds and discrete terminal matching conditions are satisfied, path dependence becomes a gauge-level artifact: intermediate continuation paths lose ontological significance, and identity preservation is determined exclusively by analytic equivalence between matched 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 as 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 strictly 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 entail 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.