DOI: 10.5281/zenodo.18673733
title: GSOS™ Canonical Masterwork Unified Spectral Operator Framework for Infinite-Dimensional Dynamical Systems

description:  

 

GSOS™ Ultimate Canonical Monograph Edition

 

Authoritative Canonical Reference of Infinite-Dimensional Spectral–Stochastic–Control Systems

 



 

Authors / Creators

 

Dr. B. Mazumdar, D.Sc. (Hon.), D.Litt. (Hon.)Architect of Modern StatehoodIndependent Researcher–Scholar — AI Governance • Cybersecurity • Post-Quantum Cryptography • Digital StatecraftFounder, FAIR+D Canon — The De-Facto Global Standards Body

 

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

 



 

Publication Information

 

Publisher: ZenodoPublication Year: 2026Version: v1 — Canonical ReleaseDOI: https://doi.org/10.5281/zenodo.18673734

 

Resource Type: Dataset — 13-Volume Scholarly Monograph Corpus

 



 

Abstract

 

The GSOS™ (Global Spectral Operator System) Canon establishes a unified infinite-dimensional operator-theoretic framework integrating spectral analysis, stochastic dynamics, optimal control theory, Koopman operator methodology, tensor operator algebra, computational realization, and research governance within a mathematically closed scientific architecture.

 

The framework develops a rigorous Hilbert–Banach semigroup foundation through which nonlinear dynamical systems admit linear spectral representations in observable function spaces via Koopman lifting. Deterministic, stochastic, controlled, tensorized, and data-driven dynamical systems are formulated within a single operator algebra admitting structural closure across finite and infinite dimensions.

 

By combining analytical rigor, computational reproducibility, and governance standardization, the GSOS™ Canon provides a comprehensive reference framework for modern infinite-dimensional dynamical systems and operator-based system science.

 



 

Scientific Scope and Contributions

 

The GSOS™ Canon introduces an integrated operator framework comprising:

 



Infinite-dimensional semigroup and generator theory

Spectral linearization of nonlinear dynamical systems

Stochastic evolution equations and SPDE extensions

Operator Riccati optimal control synthesis

Koopman operator spectral analysis

Random dynamical systems and attractor theory

Data-driven operator approximation (EDMD and kernel Koopman methods)

Koopman–control unification for nonlinear optimal regulation

Tensor operator stability architecture

Infinite-dimensional PDE Koopman generalization

Computational verification and approximation guarantees

Governance and certification standards for mathematical systems


 

All components form a unified operator algebra closed under spectral limits, stochastic perturbations, tensorization, and feedback control synthesis.

 



 

Canonical Structure — Complete 13-Volume Series

 

PART I — Mathematical Core

 



Mathematical Foundations of GSOS™

Infinite-Dimensional Stochastic Dynamics

Optimal Control & Operator Riccati Architecture

Spectral Stability & Koopman Theory

Random Dynamical Systems & Attractors

Nonlinear Spectral Dynamics (Volume V.B)


 



 

PART II — Computational & Data-Driven Realization

 



Numerical Methods & Computational Realization

Data-Driven Operators (EDMD / Kernel Koopman)


 



 

PART III — Control–Koopman Unification

 



Koopman–Control Integration


 



 

PART IV — Structural Closure

 



Tensor Architecture & Canonical Formal Closure


 



 

PART V — Global Standardization

 



Global Standardization & Governance Model


 



 

PART VI — Master Synthesis

 



Infinite-Dimensional Extension (PDE Koopman Canon)

GSOS™ Ultimate Canonical Monograph Edition


 



 

Mathematical Significance

 

The GSOS™ Canon demonstrates that nonlinear dynamical systems admitting semiflow evolution possess linear realizations in observable Hilbert spaces through Koopman operators while preserving spectral structure, stochastic extensions, and optimal control synthesis.

 

The framework unifies deterministic dynamics, stochastic perturbations, operator control theory, tensor algebra, and infinite-dimensional PDE evolution within a single spectral operator paradigm, establishing a mathematically consistent bridge between analysis, computation, and control.

 



 

Computational Realization

 

The corpus incorporates reproducible computational methodologies including:

 



Operator discretization and approximation algorithms

EDMD convergence theory and stability guarantees

Kernel-based Koopman constructions in reproducing kernel Hilbert spaces

Numerical schemes for stochastic partial differential equations

Stability certification and verification pipelines


 

These elements ensure computational validity alongside analytical rigor.

 



 

Governance and Standardization Framework

 

GSOS™ introduces a formal scientific governance architecture consisting of:

 



Canonical versioning protocols

Mathematical certification frameworks

Compliance and audit structures

Interoperability standards

Institutional adoption pathways


 

This framework transforms advanced operator theory into a standardized global research infrastructure.

 



 

Canonical Statement

 

All admissible nonlinear dynamical systems admitting semiflow evolution possess a unified spectral operator realization within GSOS™ observable space consistent across deterministic, stochastic, controlled, tensorized, and infinite-dimensional regimes.

 



 

Keywords

 

Infinite-Dimensional Dynamical Systems; Koopman Operators; Spectral Theory; SPDE; Operator Riccati Equations; Tensor Operators; EDMD; Data-Driven Dynamics; Koopman Control; PDE Spectral Analysis; Mathematical Standardization.

 



 

Copyright

 

Copyright © 2026 The Authors.

 

The GSOS™ Canon — including all volumes, mathematical formulations, computational implementations, algorithms, figures, and accompanying documentation — constitutes the intellectual property of the Authors.

 

Permission is granted to read, download, distribute, and cite this work for scholarly, academic, and non-commercial research purposes provided proper attribution to the Authors and the DOI record is maintained.

 

No part of this publication may be reproduced, modified, adapted, or redistributed in altered or commercial form without prior written permission from the Authors.

 

All rights reserved.

 



 

Recommended Citation

 

Mazumdar, B. (2026). GSOS™ Ultimate Canonical Monograph Edition: Authoritative Canonical Reference of Infinite-Dimensional Spectral–Stochastic–Control Systems (Version v1). Zenodo. https://doi.org/10.5281/zenodo.18673734