This document explores a fundamental paradigm shift in computational theory, moving beyond classical Boolean and quantum unitary architectures toward a generalized framework based on symplectic geometry. It establishes the "symplectic computational ontology," which utilizes the non-compact symplectic group to achieve enhanced expressivity and robustness compared to standard complex-Hilbert space models. The analysis systematically formalizes the quantum-symplectic duality, investigates non-linear dynamical regimes through canonoid transformations and bi-Hamiltonian structures, and extends these principles to infinite-dimensional field-theoretic and non-Archimedean $p$-adic arithmetic spaces. Furthermore, it details how categorical tools, such as Fukaya categories and gentle algebras, can compress complex topological data into executable combinatorial algorithms. Finally, the volume addresses the profound geopolitical consequences of this technological transition, arguing that the emergence of advanced symplectic KSCCN Mamun, SM (2026) …………………………..1 The Symplectic Computational Ontology: From Infinite-Dimensional Geometries and Categorical Algebra to Geopolitical Sovereignty (Vol-I) K S C and categorical AI architectures necessitates new decolonial frameworks to protect epistemic and infrastructural sovereignty against systemic data extraction and digital colonialism. Also available on Academia.edu: https://www.academia.edu/attachments/133170160/download_file?s=portfolio
This document explores a fundamental paradigm shift in computational theory, moving beyond classical Boolean and quantum unitary architectures toward a generalized framework based on symplectic geometry. It establishes the "symplectic computational ontology," which utilizes the non-compact symplectic group to achieve enhanced expressivity and robustness compared to standard complex-Hilbert space models. The analysis systematically formalizes the quantum-symplectic duality, investigates non-linear dynamical regimes through canonoid transformations and bi-Hamiltonian structures, and extends these principles to infinite-dimensional field-theoretic and non-Archimedean p-adic arithmetic spaces. Furthermore, it details how categorical tools, such as Fukaya categories and gentle algebras, can compress complex topological data into executable combinatorial algorithms. Finally, the volume addresses the profound geopolitical consequences of this technological transition, arguing that the emergence of advanced symplectic KSCCN Mamun, SM (2026) …………………………..1 The Symplectic Computational Ontology: From Infinite-Dimensional Geometries and Categorical Algebra to Geopolitical Sovereignty (Vol-I) K S C and categorical AI architectures necessitates new decolonial frameworks to protect epistemic and infrastructural sovereignty against systemic data extraction and digital colonialism. Also available on Academia.edu: https://www.academia.edu/attachments/133170160/download_file?s=portfolio
Building upon the theoretical foundations established in Volume I, this second volume transitions from ontological formalism to engineering realization and geopolitical implementation. It addresses the critical hardware bottleneck and infrastructural sovereignty risks identified in the symplectic computational framework. The volume details the design of native symplectic processors ("symplectic foundries") capable of processing symbits through analog optical lattices and non-linear media, implementing canonoid transformations physically rather than through simulation. It introduces the "Gentle Compiler" architecture for translating categorical structures (Fukaya categories, Ginzburg dg algebras, gentle algebras) into executable hardware control sequences. A comprehensive "Silicon Bandung" roadmap is presented for establishing sovereign semiconductor capabilities in the Global South, alongside protocols for the "Zero Digital Divide" initiative to ensure representative datasets and participatory epistemic agency. The work culminates in a proposed global treaty architecture for infrastructural sovereignty, ensuring that the transition to post-unitary computing architectures fosters a genuinely multipolar computational order rather than entrenching new forms of digital colonialism. Also available on Academia.edu: https://www.academia.edu/attachments/133170185/download_file?s=portfolio
The second quantum revolution represents a seminal rupture in global governance, international relations, and socio-economic organization. As quantum computing, communication, and sensing technologies transition from laboratory prototypes to strategic national assets, traditional classical and Newtonian regulatory frameworks are proving fundamentally ill-equipped to address their non-local, probabilistic, and dual-use nature. This report synthesizes the epistemological shift from substance-based to relational, quantum-coherent ontologies, proposing a new framework for "quantum-coherent governance" that embraces relational complexity and adaptive uncertainty. By analyzing the divergent evolutionary trajectories of the United States, China, Germany/EU, Japan, South Korea, and Russia, the analysis highlights the emergence of trilateral security alignments and the critical risks posed by a potential "quantum splinternet." The report concludes that without inclusive, multi-layered institutional architectures, the transition to fault-tolerant, utility-scale quantum deployment threatens to entrench global epistemic injustice and asymmetric geopolitical vulnerabilities. KSCCN Mamun, SM (2026) ………………………………………….1 A Comprehensive Theory of Quantum Governance: Ontological Shifts, Multipolar Evolutionary Trajectories, and Future Scenarios in the Second Quantum Revolution (Vol-V) Also available on Academia.edu: https://www.academia.edu/attachments/133194537/download_file?s=portfolio
This report examines the ontological foundations of quantum mechanics, challenging the notion that geometric space and classical subsystems are primordial axioms of nature. By integrating algebraic quantum mechanics, quantum mereology, discrete homology, and topos theory, the study demonstrates that these features emerge dynamically from purely quantum mechanical precursors. The synthesis utilizes the Gelfand-Naimark-Segal (GNS) construction to derive geometric Hilbert spaces from abstract algebraic relations, effectively relegating the Hilbert space to a derived and contingent structure rather than a fundamental one. The research further employs a "basic shapes" paradigm in discrete homology to efficiently compute the higher-order structures of complex networks, bypassing the exponential computational bottlenecks traditionally associated with high-dimensional topological analysis. By identifying a minimal universal set of atomic configurations, such as the triangular prism or the discrete hypercube, the dimensionality of the boundary matrix is collapsed, achieving median speedups of 47.5x over previous algorithms. KSCCN Mamun, SM (2026) ………………………………….1 Algebraic, Topological, and Mereological Foundations of Quantum Information: A Synthetic Framework for Emergent Geometry, Computational Physics, and Cosmology K S C Furthermore, the report establishes a link between subatomic gauge symmetries and cosmological dark energy through the Axion-Modulated Quintessence framework. Also available on Academia.edu: https://www.academia.edu/attachments/133038377/download_file?s=portfolio
This anatomical review critically dissects Igor Volovich's (2024) proposal for symplectic computers, a conceptual framework grounded in the quantum-symplectic duality. By reformulating the Schrödinger equation in real variables, Volovich reveals that unitary quantum evolution is embedded within the larger symplectic group Sp(2N, ℝ). The review evaluates the paper's mathematical structure, the introduction of symplectic bits (symbits), and the canonical embedding map γ : U(N) → Sp(2N, ℝ). While acknowledging the elegance of the duality, the analysis identifies significant gaps in the formal definition of a computational model, the absence of complexity-theoretic grounding for claimed superiority, and ambiguities in scaling from single symbits to multi-symbit registers. Comparative analysis situates the work within emerging geometric approaches to quantum and classical computation. Profound epistemological questions arise concerning the privileging of complex Hilbert spaces, alongside ontological implications for the quantum-classical boundary. This Volume I initiates a multi-volume research program aimed at rigorous formalization and exploration of symplectic computation as a potential post-quantum paradigm. K S C Also available on Academia.edu: https://www.academia.edu/attachments/133164750/download_file?s=portfolio
The advent of cryptanalytically relevant quantum computers (CRQCs) threatens the foundational mathematical hardness assumptions of contemporary public-key cryptography. In response, Post-Quantum Cryptography (PQC) has emerged, predominantly framed through an epistemic lens of "algorithmic substitution"—replacing vulnerable algorithms with quantum-resistant ones. However, for sovereign entities and developing digital infrastructures, this universalist approach is insufficient. This paper conducts a deep epistemic analysis of the shift toward layered architectural resilience, cognitive sovereignty, and cybernetic governance. It proposes a foundational set of normative principles for a sovereign PQC protocol and systematically compares ten competing theories in cryptography, digital sovereignty, and data architecture. K Also available on Academia.edu: https://www.academia.edu/attachments/134141335/download_file?s=portfolio
K SC The second quantum revolution is not only a scientific and technological transformation but also a profound governance challenge. As quantum technologies move from laboratory demonstrations to strategic assets, states and international institutions face urgent questions about security, sovereignty, standards, supply chains, and ethical deployment. This third volume in the series examines the emerging field of quantum governance through the lenses of international relations, science and technology studies, and digital sovereignty. It analyses the competitive dynamics between major powers, the risks of quantum-enabled disruption to existing security architectures, and the opportunities for more equitable global regimes. Particular attention is given to the position of the Global South and to the institutional innovations required to prevent a quantum divide that mirrors or deepens existing inequalities. The paper argues for a multi-layered governance architecture that combines arms-control-like mechanisms for quantum capabilities with proactive investment in inclusive quantum infrastructure and norms. Also available on Academia.edu: https://www.academia.edu/attachments/133209098/download_file?s=portfolio