DOI: 10.5281/zenodo.18719659
title: GNSA-26: Global Neuro-Sovereignty Architecture — Mathematical Foundations, Control Systems, Observer Theory, and Governance Framework

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Title

GNSA-26: Global Neuro-Sovereignty Architecture — Mathematical Foundations, Control Systems, Observer Theory, and Governance Framework



DOI

10.5281/zenodo.18719659

ORCID

https://orcid.org/0009-0007-5615-3558



Author

Dr. B. Mazumdar, D.Sc. (Hon.), D.Litt. (Hon.)Independent Research Scholar & Architect of Modern StatehoodFounder & Principal Architect, FAIR+D Canon™ — Proprietary Sovereign Systems Architecture & Governance Framework



Abstract

This work presents a rigorously formalized, fully integrated scientific and governance architecture for Global Neuro-Sovereignty, combining advanced mathematical control theory, stochastic observer systems, nonlinear stability analysis, delay-dependent robustness certification, distributed networked estimation, cryptographic governance logic, and international legal–institutional design.

The framework establishes a unified doctrine integrating nonlinear control systems, stochastic stability theory, Extended Kalman Filter (EKF) Lyapunov architectures, generalized polynomial chaos (gPC) uncertainty propagation, distributed observer consensus, Byzantine-resilient network design, and treaty-grade governance mechanisms, yielding a closed, coherent, and computationally verifiable canonical system.

All theoretical developments are derived using first-principles mathematical rigor, formal Lyapunov synthesis, convex optimization, Riccati-based observer design, and certified delay-dependent Linear Matrix Inequality (LMI) methods. Complete deterministic and stochastic Python implementations accompany the theoretical framework, enabling full computational validation and reproducibility.

This canonical set establishes a mathematically provable foundation for neuro-infrastructure security, cognitive sovereignty, AI-driven neural systems governance, treaty-grade institutional compliance, and planetary-scale observer networks, unifying physical system theory with legal–institutional architectures in a single integrated scientific framework.



Canonical Scope and Structure

PDF 1 — Core Scientific Architecture

Volume I — System Foundations & Control Architecture



Nonlinear dynamical modeling

Stochastic stability theory

Delay-dependent Lyapunov synthesis

Riccati-based observer and controller design

Spectral robustness margins

Full computational verification


Volume II — Advanced Observer & Uncertainty Theory



Extended Kalman Filter (EKF) nonlinear stability proofs

Delay-dependent observer synthesis

Distributed and networked observer consensus

Generalized polynomial chaos (gPC) uncertainty propagation

Mean-square exponential stability certification

Convex LMI robustness validation

Full computational demonstration




PDF 2 — Treaty, Governance & Institutional Architecture



Formal legal codification of neuro-sovereignty

Cognitive rights, consent governance, and mental privacy doctrines

Oversight authority and compliance audit architecture

Institutional enforcement logic

Cryptographic compliance verification engines




PDF 3 — AI-Driven Neuro-Infrastructure & BCI Governance



Neural dynamics modeling

Secure control and resilience engineering

Byzantine-resilient distributed systems

Intrusion detection and anomaly certification

Formal safety, override, and governance constraints




Annex Series (A–F) — Formal Proofs, Algorithms & Computational Frameworks



Extended mathematical derivations

Full Python-based numerical validation

Simulation architectures and verification pipelines




Technical Foundations



Nonlinear dynamical systems

Stochastic differential equations

Lyapunov stability theory

Delay-dependent control

Extended Kalman filtering

Distributed observer networks

Polynomial chaos expansions

Convex optimization and LMI synthesis

Formal legal–technical codification

Cryptographic compliance architectures




Computational Architecture

All theoretical developments are accompanied by fully reproducible Python implementations, including:



Riccati solvers and LMI optimization

EKF simulation and nonlinear convergence verification

Monte-Carlo stability testing

Delay margin computation

Distributed consensus and Byzantine fault modeling

Compliance audit engines

Consent governance logic




Contribution Statement

This canonical work establishes a complete mathematical, computational, and governance framework for neuro-sovereignty systems, unifying control theory, observer design, stochastic stability, distributed computation, cryptographic governance, and international legal architecture into a single formal doctrine.

The framework enables provably secure, resilient, and governable neuro-infrastructure systems suitable for civil, medical, institutional, and planetary-scale applications.



Keywords

Neuro-Sovereignty; Nonlinear Control; Stochastic Stability; Lyapunov Theory; Extended Kalman Filter; Distributed Observers; Delay Systems; LMI Optimization; Governance Architecture; Treaty Design; Cognitive Rights; AI Governance; Cryptographic Compliance; Institutional Systems Engineering.



License & Rights

Copyright © 2026 The Author.All rights reserved under FAIR+D Canon™ Proprietary Sovereign Systems Architecture & Governance Framework.