The Axiomatic Theory of Cyber-Physical Stability, Joint Controllability and Human Custodianship in Distributed Machine-Native Economies

ANOA — Essay IX | Independent Theoretical Working Paper This paper develops an axiomatic and mathematical framework for the stability, security, controllability, and human accountability of distributed machine-native economies. Building upon the ANOA (AI-Native Organizational Architecture) research programme, the study examines the interdependence of autonomous financial agents, distributed computational networks, industrial Internet of Things (IoT) systems, operational technology (OT), and critical economic infrastructures. The theoretical framework integrates spectral stability analysis, agent-based modelling protocols, public–private controllability, cyber-physical risk propagation, post-quantum cryptographic resilience, and rights-constrained human intervention. Particular attention is devoted to the conditions under which individually stable subsystems may become unstable through network interdependencies, and to the mathematical limitations of isolated monetary, technological, and institutional control mechanisms. The paper further introduces a human custodianship framework informed by Stoic principles of practical wisdom, justice, temperance, responsibility, and disciplined authority. These principles are translated into institutional design constraints rather than treated as substitutes for mathematical or empirical validation. HomeSelf and the VPR (Verifiable Property Representation) framework are discussed as prospective architectural application contexts, particularly regarding economic interoperability, representation integrity, provenance, authorization, and human oversight. The study distinguishes formal mathematical results from architectural proposals and untested empirical hypotheses. Its computational experiments, cryptographic migration assessments, and cyber-physical validation procedures constitute a proposed research agenda rather than completed experimental findings. Research classification: Independent theoretical working paper. Version: 1.0 DOI: 10.5281/zenodo.23971609 Author: Marco Patrone Copyright: © 2026 Marco Patrone. All rights reserved. This research does not imply institutional endorsement, regulatory approval, or operational certification by any organization referenced in the manuscript.