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Anthropomorphism as Geodesic Projection: A Quantum-Information Geometric and Hamiltonian Synthesis for Emergent Intersubjectivity in Heterogeneous Multi-Agent Systems

Syed Muntasir Mamun

Published Jan 1, 2026• 0 citations
Publisher

Abstract

The engineering of distributed cognition in heterogeneous multi-agent systems (MAS), including human-AI collaborations, requires a theoretical framework that accounts for the limitations of classical information processing, specifically the phenomena of contextuality, order effects in reasoning, and the non-separability of semantic states. This paper fundamentally extends the foundational "Anthropomorphism as Geodesic Projection" paradigm—which reframed anthropomorphism as a structural necessity or "interactive grammar" for synthesizing cognitive processes—by incorporating a quantum dimension. We posit that the irreducible non-commutativity of cognitive states Mamun, SM (2026) ………………………………………….1 Anthropomorphism as Geodesic Projection: A Quantum-Information Geometric and Hamiltonian Synthesis for Emergent Intersubjectivity in Heterogeneous Multi-Agent Systems necessitates a shift from classical geometry to Quantum Information Geometry. The framework transitions from the classical Fisher-Rao metric to the Bures-Wasserstein and Wigner-Yanase-Dyson (WYD) metrics, embedding agent distributions onto a quantum statistical manifold endowed with a non-commutative algebra of observables. Dynamical flows are derived via a Quantum Hamiltonian formulation governed by the Schrödinger-von Neumann equation, replacing the classical, commutative Poisson dynamics with non-commutative commutators. Also available on Academia.edu: https://www.academia.edu/attachments/131737100/download_file?s=portfolio

DOI
10.5281/zenodo.22993304

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N C K SC K SC Recent advances at the intersection of quantum information geometry and machine-learning approaches to the renormalisation group suggest a fertile reinterpretation of the Similarity Renormalization Group (SRG). The continuous unitary transformations that drive a Hamiltonian toward band-diagonal form may be viewed as geodesics on a manifold of quantum states (or of density operators) equipped with a monotone metric, or equivalently as successive layers of a deep network that progressively disentangle degrees of freedom. This independent study develops that correspondence. It reviews the information-geometric structures relevant to quantum field theories and many-body Hamiltonians, examines neural-network renormalisation-group (NN-RG) architectures, and maps the SRG flow—originally clarified in the pedagogical setting of Szpigel & Perry (2000)—onto both geometric and learning-theoretic languages. The resulting perspective yields analytic insights into the optimality of particular generators and practical algorithms for approximate Hamiltonian diagonalisation that combine SRG ideas with modern differentiable programming. Error-scaling diagnostics originating in the two-dimensional laboratory are re-expressed as statements about geodesic deviation and about generalisation error in the associated learning problem. Also available on Academia.edu: https://www.academia.edu/attachments/133749950/download_file?s=portfolio
This paper synthesizes the "Anatomical Reviews" to redefine the quantum-classical transition through an intrinsic operator-algebraic framework. It moves away from standard environment-induced decoherence toward a model where classicality emerges from the sectorisation of infinite-dimensional Hilbert spaces within isolated systems. Utilizing the Avalanche Photodiode (APD) model, the study demonstrates that macroscopic definiteness arises from double-exponential divergence in state overlap, creating a rigorous structural transition. The work formalizes this transition as a geometric degeneracy in the quantum Fisher information metric, linking fractal avalanche geometry to Tomita-Takesaki modular theory and providing a falsifiable experimental foundation for the algebraic Heisenberg cut. KSCCN Mamun, SM (2026) ……………………………….1 Algebraic Sectorisation, Information Geometry, and the Quantum-Classical Transition A Synthesis of the Anatomical Reviews (Vol-VI) Also available on Academia.edu: https://www.academia.edu/attachments/133083183/download_file?s=portfolio