Q-FENG: A Cybernetic Neurosymbolic Framework for AI Governance Monitoring via Hilbert-Space Interference — Empirical Validation Through Adversarial CLT Extension and Manaus O₂ Crisis Retrospective

Q-FENG (Quantum-Fractal Neurosymbolic Governance) is a cybernetic neurosymbolic framework for AI governance monitoring that operationalises normative friction as an interference angle θ in a Hilbert-space representation of predictor and normative states. The framework integrates Stafford Beer's Viable System Model, Quantum Decision Theory (Born rule with interference term), and Answer Set Programming (Clingo) into a five-stage pipeline that classifies governance regimes into three categories: STAC (θ < 30°, autonomous operation), HITL (30° ≤ θ < 120°, human-in-the-loop escalation), and Circuit-Breaker (θ ≥ 120°, blocked execution). This paper presents the empirical validation of Q-FENG across two domains of public-sector AI deployment in Brazil: health resource allocation (SUS specialist services, including the 2021 Manaus oxygen crisis) and labour law adjudication (Consolidação das Leis do Trabalho — CLT). Validation strata The validation comprises three independent strata: Seven authored proof-of-concept scenarios spanning Brazilian SUS, US Medicaid (Obermeyer), and Brazilian CLT. Five scenarios were classified CIRCUIT_BREAKER (θ ∈ [127.8°, 134.7°]) and two STAC positive controls (θ < 8°), demonstrating the discriminability of the geometric formalism. A 70-epidemiological-week retrospective analysis of the Manaus 2020–2021 hospital collapse, in which Q-FENG sustained stable CIRCUIT_BREAKER classification with first stable onset at SE 37/2020 — 19 weeks before the state-level public calamity declaration of January 2021. An adversarial CLT extension comprising 3,700 jobs (four architectural arms: B1 unstructured baseline, B3-novo deterministic Clingo, B4-novo-v2 NeSy 1.0 verifier-passive anchoring, and B5_SIDECAR_v2 Q-FENG full sidecar; 100 scenarios × 4 LLM backbones × 3 random seeds per arm) with pre-registered Bonferroni-corrected hypotheses (m=7, α_corrected = 0.00714). The full Q-FENG sidecar demonstrates Variety Amplification V(B5)/V(B1) = 7/3 = 2.33 over the unstructured baseline. Canonical contributions The paper introduces four canonical contributions: A quantum interference geometry for normative alignment via Hilbert-space inner products A Markovian θ-efetivo extension for temporal governance tracking A failure typology grounded in positive law (constitutional, execution-inertia, execution-absent-channel) An architectural category γ for AI governance sidecars demonstrated through ablation The framework operates within the EU AI Act regulatory perimeter (Regulation 2024/1689) and provides a reproducible reference implementation for the high-risk public-sector AI use cases enumerated therein. Theoretical foundation The framework operationalised in this paper is theoretically grounded in Kaminski (2026a), A Governança Cibernética da Inteligência Artificial: Do Compliance ao Controle (independently published, KDP: https://www.amazon.com/dp/B0GX33QDTZ). The book establishes the tripartite governance taxonomy (Type I principled, Type II risk-management, Type III cybernetic) and identifies the empirical absence of Type III implementations that the present paper addresses through the Q-FENG proof-of-concept pipeline. Editorial history An earlier working-paper version is available on SSRN (DOI: 10.2139/ssrn.6433122). The present Zenodo deposit is the revised and expanded version, incorporating the adversarial CLT extension (3,700 jobs across four architectural arms) and the 70-epidemiological-week Manaus O2 Crisis retrospective. Code and data availability Companion repository (private, access by invitation): https://github.com/Ricardo-Kaminski/qfeng_validation. All parquet result files, Clingo corpus, and pipeline code are included. Reproducibility is guaranteed via deterministic Clingo evaluation, SHA-256 cached DeonticAtoms, and fixed random seeds documented in the pre-registration.