Δ𝓘 = 0: The Minimal Principle of Ontological Motion

We introduce what we call an ontological topological jump protocol: an interpretive and operational framework in which effective displacements between configurations arise from analytically protected identity continuation, rather than from force-driven motion or traversal along continuous Euclidean paths. In this setting, persistence is not attributed to dynamical transport through space, but to the preservation of identity under complex-analytic continuation subject to structural constraints. The central structural conclusion is that sustained, non-collapsing evolution is ontologically realizable if and only if the system admits a complex-analytic representation equipped with a real-valued identity functional I, whose discrepancy vanishes under protected continuation. When such analytic protection holds and discrete terminal matching is satisfied, path dependence is demoted to a gauge-level artifact: intermediate continuation paths lose ontological significance, and identity preservation is determined entirely by analytic equivalence between matched endpoints. Within this framework, physical evolution is modeled as analytic continuation on a complex manifold, while observed spacetime trajectories arise only as projections of this higher-dimensional analytic structure. The protocol permits consistent re-identification between spatially separated configurations without requiring a unique continuous Euclidean trajectory, provided analytic protection and endpoint matching are maintained. Operationally, the protocol manifests through three interrelated structural effects:(i) suppression of net analytic drift via local compensation mechanisms;(ii) controlled continuation around singular structures; and(iii) holomorphic correlation enforcing identity closure between entrance and exit configurations.These effects are not introduced as independent axioms, but emerge as explanatory consequences of the analytic framework. We provide a concrete realization using the Riemann zeta function. Numerical results demonstrate that a nontrivial invariant constructed from the arguments of zeta(s) and zeta′(s) satisfies loop invariance, endpoint stability under matched continuation, and strong suppression of interior variation along protected paths. Additionally, protected path costs exhibit quadratic scaling, consistent with conservative analytic dynamics. Within this structural regime, apparent nonlocal or superluminal features arise strictly as projection effects of analytically protected continuation, rather than from signal propagation or force-mediated transport. At the level considered here, the protocol does not violate causality or conservation laws; instead, it reframes transport as a problem of identity consistency governed by complex analysis and topological closure, rather than by Euclidean traversal. The framework reframes apparent non-local effects as consequences of analytic identity equivalence, offering a mathematical perspective on the emergence of spacetime from deeper arithmetic structure.