Operating in the framework of `supmech' (a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic geometry and noncommutative probability in an algebraic setting, it associates, with every `experimentally accessible' system, a symplectic algebra and operates essentially as noncommutative Hamiltonian mechanics with some extra sophistication in the treatment of states) it is shown that interaction between systems can be consistently described only if either (i) all system algebras are commutative or (ii) all system algebras are noncommutative and have a quantum symplectic structure characterized by a UNIVERSAL Planck type real-valued constant of the dimension of action.
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