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Collective Intelligence as Geometric Projection: Swarm Dynamics, Reinforcement Learning Equivalence, and the Topological Unification of Distributed Cognition

Submitted:

11 December 2025

Posted:

12 December 2025

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Abstract
The phenomenon of collective intelligence in biological swarms has traditionally been explained through emergentist paradigms, where complex global behaviors arise from simple local interactions. This paper presents an alternative geometric interpretation grounded in the Timeless Counterspace \& Shadow Gravity (TCGS)-SEQUENTION framework, proposing that collective behavior is fundamentally a projection artifact of a higher-dimensional static structure rather than an emergent property. We synthesize three independent lines of empirical research: (i) the mathematical proof by Soma et al.\ that honeybee swarm decision-making is equivalent to a single reinforcement learning agent, (ii) the demonstration by Vellinger et al.\ that stigmergic coordination in \textit{C.\ elegans} corresponds to Cross-Learning algorithms, and (iii) the Mean Feature Embedding approach of H\"uttenrauch et al.\ for permutation-invariant swarm representations. Within the TCGS ontology, these findings receive unified geometric interpretation: the ``single agent'' identified in swarm dynamics corresponds to a four-dimensional source singularity, pheromone fields constitute the physical instantiation of projected potentials, and invariant embeddings represent slice-independent geometric observables. We derive a single Extrinsic Constitutive Law for biological swarms that replaces the concept of ``emergence'' with ``projection,'' offering a deterministic, geometric resolution to the Combination Problem in collective cognition. The framework generates testable predictions regarding non-local correlations in partitioned colonies, critical acceleration scales in flocking dynamics, and decoherence thresholds in rapidly changing environments.
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Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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