ฮ๐ = 0: The Minimal Principle of Ontokinesis
Abstract
We propose $\Delta\mathcal{I}=0$ as a minimal closure principle for ontological motion: identity is preserved precisely when a wrapped analytic invariant exhibits vanishing discrepancy under a protected continuation protocol with terminal matching. This yields an operational criterion for persistence: a system must admit a complex-analytic representation equipped with a real-valued identity functional whose loop drift is suppressed and whose boundary values match discretely. We formalize a strict three-layer separation: (i) a theorem layer (existence of a closure invariant), (ii) a protocol layer (projection-agnostic identity certification), and (iii) an implementation layer (a concrete realization on the Zeta Manifold). Physical interpretation is explicitly excluded from the theorem layer. We implement the protocol using a holomorphic ledger family built from $\zeta$ and $\zeta'$. Numerical experiments demonstrate loop invariance, discrete terminal ports, echo-closed strongly connected components, round-trip consistency, and a large port-uniqueness gap (separation of approximately four orders of magnitude), establishing $\Delta\mathcal{I}=0$ as a closed operational principle.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Neural Networks and Reservoir Computing
advanced mathematical theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 1 January 2026