Management and Regulation of Artificial Intelligence Models in Public Administration: Cryptographic Transparency and Digitalization of Legal Norms

This paper proposes a conceptual methodological framework based on a Dual-Domain Architecture mediated by a Zero-Knowledge Audit Proxy (ZKAP) to reconcile AI Act accountability with GDPR data minimization. Legal norms are polynomialized into R1CS constraints, transforming compliance into a formally verifiable computational property. For cognitively opaque exascale models, these invariants may be hardware-anchored through a Provable Arithmetic Logic Unit (pALU), ensuring determinism and resistance to algorithmic drift. For lower-risk or on-premise systems, ZKAP operates in a software-only configuration, enabling periodic asymmetric regulatory proofs without silicon-level integration. A calibrated threshold distinguishes admissible technical variance from structural divergence, triggering mandatory safeguards. The framework provides a proportional, scalable, and cryptographically verifiable oversight model applicable both to future non-explainable AI systems and to lighter local infrastructures. This Zenodo deposit contains both the original Bulgarian peer-reviewed version (version of record) and an unofficial English translation. The Bulgarian version was published in Artificial Intelligence Proceedings (ISSN 3033-2923 / 3134-1667), pp. 75–78, as presented at the XI International Scientific Conference "High Technologies. Business. Society", Borovets, Bulgaria, 23–26 March 2026.