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June 14, 20260 citationsOpen Access

Multidimensional Telotopic Space: A Computational Ontological Standard for Cognitive Science and AI

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AKAlan Kleden

Key Points

  • The study aims to extend axiodynamic formulations of affect-cognition dynamics for better modeling of multi-agent interactions.
  • Generalized telotopic space from one to multiple dimensions.
  • Developed a coherence tensor to encode the coupling structure of teloi.
  • Formulated temporal dynamics with specific operators for inter-agent interactions.
  • Outlined a four-level admissibility hierarchy for the formalism.
  • Derived new tensorial predictions distinct from previous models.
  • Established spectral signatures for regime transitions within the framework.

Abstract

Existing axiodynamic formulations model affect-cognition dynamics as directional coherence relative to a single operative telos, adequate for individual decision-making but insufficient for interaction, where several concurrent teloi couple and evolve in time. This paper extends the framework to dyadic and multi-agent dynamics while preserving the nine-axiom hard core. Five contributions are developed. The telotopic space is generalized from one angular dimension to concurrent dimensions, with the active telos defined as the principal eigenvector of a weighted scatter operator under an explicit spectral-resolution condition. A symmetric positive semi-definite coherence tensor encodes the coupling structure of concurrent teloi, and a conditional theorem establishes the spectral signatures of regime transition. The temporal and inter-agent dynamics - arbitration operator, intertemporal affective accumulator, sparse attentional architecture - are formalized, with the canonical dyadic case integrating a vectorial axiological distance. A four-level admissibility hierarchy (CAT) delimits the formalism's scope and articulates with the necessary and sufficient condition for teleonomic classification. Finally, a family of falsifiable tensorial predictions is derived, distinct from existing mémotion-level and architecture-level predictions. The framework is offered as a computational ontological standard for affect-cognition dynamics across biological and artificial substrates, with its open problems stated as well-formed empirical questions.

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Cite This Study

Alan Kleden (2026) studied this question.

synapsesocial.com/papers/6a2e4753b1cc60ccdea8be01https://doi.org/10.5281/zenodo.20667618
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