Publication briefs
Author: Rui A. P. Perdigão
Date: December 2025
Title: Generalized Categorical Physical Intelligence (GCPI): Deciphering Non-Ergodic Nonlinear Nonlocal Multiscale Spatiotemporal Neo-Systemic Complexity and Predictability.
DOI: https://doi.org/10.46337/251213
Indexed: Yes (Crossref)
Cite as:
Perdigão, R.A.P. (2025): Generalized Categorical Physical Intelligence (GCPI): Deciphering Non-Ergodic Nonlinear Nonlocal Multiscale Spatiotemporal Neo-Systemic Complexity and Predictability. https://doi.org/10.46337/251213
Methodological Keywords: Categorical Algebra, Exterior Algebras, Higher-Order Algebraic Structures, Systems Intelligence, Mathematical Physics, Information Physics, Information Theory, Complex Systems, Data Assimilation, Model Design.
Applied Keywords: Scaling, Multifractals, Aerospace Engineering, Big Data Analytics, Artificial Intelligence, Physical Intelligence, Machine Learning, Natural Hazards, Extreme Events, Quantum Information Technologies, Quantum Satellites, Quantum Constellation, Quantum Sensing, Quantum Simulation, Multi-Hazards.
Summary
A novel information physical system dynamic intelligence methodological suite is hereby introduced for retrieving, analyzing, processing and predicting the emergence of generalized spatiotemporal non-ergodic nonlocal nonlinear multiscaling mechanisms in complex system dynamics.
Our new Generalized Categorical Physical Intelligence (GCPI) is constructed enabling the formalization of broader classes of structural-functional interactions and symmetries, along with the prediction of non-recurring critical transitions, symmetry breaks and neo-systemic emergence elusive to prior data records or state-of-art formalisms, shedding light onto system dynamics and predictability even in the absence of the traditional anchoring foundational spaces and symmetries.
Traditional vector, functional or operator space requirements are lifted, as are exponential scaling mechanisms and classical symmetries, thereby allowing for a broader yet still operable construct that does not need to be commutative, distributive and not even associative.
Yet new classes of physically interpretable morphisms and symmetries are unveiled from our GCPI that allow for a full-fledged physically consistent generalized categorical algebra to be systematically derived and operated upon, and new features of system dynamic complexity to be formally unveiled, deciphered and treated.
Practical examples are explored including the generalization of nonlocal spatiotemporal systems exhibiting long-range dynamic entanglement, the unveiling of new classes of multifractal scaling mechanisms within spatiotemporal processes deemed non-fractal under classical algebras yet endowed with novel categorical multifractality in our broader construct, and the extending of post-critical predictability ranges beyond classical system dynamic information collapse inherent to a full structural-functional systemic overhaul.
Operational impacts are also demonstrated and discussed, including in further empowering multi-hazard risk dynamic assessments, entangled multi-extreme event prediction, early warning, prediction and decision support systems, helping further strengthen civil protection mechanisms and long-term planning in the wake of multiscale multidomain systemic disruptions across our environment and society.
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Notes
An overview of this work is also presented at the American Geophysical Union (AGU) Annual Meeting Meeting 2025, on December 16th, 2025.
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