Ξπ = 0: The Minimal Principle of Ontokinesis
Abstract
We present a minimal protocol semantics for certifying identity under analytic continuation, formalized by the principle $\Delta\mathcal{I}=0$ and termed \textit{ontokinesis}. The central object is a directed \emph{identity graph} whose edges are generated by a wrapped discrepancy test on a protocol-evaluated invariant; \emph{identity classes are defined as strongly connected components (SCCs)} of this digraph. Certification requires (i) loop invariance under protected continuation (to suppress branch drift), (ii) discrete vertex construction within bounded search windows (terminals/candidates), and (iii) echo closure as a bidirectional edge-completion rule. As a concrete implementation, we construct a holomorphic ledger family from the Riemann zeta function $\zeta$ and its derivative $\zeta'$. The protocol produces machine-verifiable certificates for loop invariance, edge separability (a port-uniqueness gap), SCC closure on finite vertex sets, and parameter windows in which SCC partitions remain stable. Throughout, ``ontokinesis'' denotes a protocol-level identity capability and carries no metaphysical commitment.
Fields of Study & Subjects
Cryptography and Data Security
Security and Verification in Computing
Advanced Authentication Protocols Security
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 1 January 2026