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arXiv · 2606.24240

Fractal Algebraic Topology of Semantic Computation. A Peer-Review-Oriented Formalization of the SSTD/BrainiaK Concept Bundle

Jean-Philippe Garnier
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Abstract

This manuscript develops material from the internal French research notes Traite de Topologie Algebrique Fractale into an academic manuscript. The editorial rule is strict: implementation names are not used as mathematical proofs, analogies are not promoted to theorems, and every formal result is either proved from explicit assumptions or downgraded to a model law, conjecture, or empirical claim. The central object is T n , a finite heterogeneous concept container formalized as a section of a product bundle whose slots include an empirical sensorimotor base R 14 , grammatical fibres, polarity, intensity, vision and audition slots, an SSTD spectral slot, a refined compositional fibre, and auxiliary tool/metric/axis/hint slots. We prove elementary structural results about product-bundle representation, heterogeneous GCM metrics, and continuity of componentwise operations. We then give conditional results for Frobenius-inspired crystal composition, Gamma/CNS curvature-Hopf modelling, Kalman convergence, SSTD bundle morphisms, and SpiderR flat-connection idealizations. Each conditional result includes its assumptions, proof status, implementation correspondence, and the boundary between mathematics, model assumptions, and empirical evidence.

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Jean-Philippe Garnier. 2026-06-23. Fractal Algebraic Topology of Semantic Computation. A Peer-Review-Oriented Formalization of the SSTD/BrainiaK Concept Bundle. https://arxiv.org/abs/2606.24240

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