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Autor principal:	Takahashi, K
Format:	Recurso digital
Idioma:	anglès
Publicat:	Zenodo 2025
Matèries:	Artificial intelligence gradient flows Mathematics Mathematical model Information Theory PFHS Persistence–First Holographic Systems Geometry Hellinger–Kantorovich distance Bures metric entropy–transport Markov chains detailed balance persistence Lyapunov functional entropy production law–time symmetry Dobrushin contraction Gibbs/DLR measures origin stabilization self–reference self–organizing intelligence statistical physics stochastic dynamics
Accés en línia:	https://doi.org/10.5281/zenodo.17706175
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This work develops a reversible variant of Persistence–First Holographic Systems (PFHS) on top of Fibered Bures–Hellinger–Kantorovich (FBHK) entropy–transport geometry. Instead of using PDEs as primitives, the paper works in the metric–measure framework of EVI (evolution variational inequality) gradient flows on the Wasserstein space of probability laws. The continuous FBHK gradient flow is discretized into a “law–time” Markov semigroup whose one–step map is represented by a Feller Markov kernel. Under explicit assumptions—FBHK geodesic geometry, λ–convex total entropy, and EVI–type contractivity—the kernel is required to be reversible with respect to a bulk invariant law, and equipped with a persistence Lyapunov functional that encodes growth of long–lived structure. On this basis, the paper defines reversible PFHS cores, bi–infinite path laws that are invariant under time reversal, and “retrocausal persistent modes” whose persistence drift has the same sign in forward and backward law–time. Observation is modelled as coarse–graining via Markov kernels satisfying a data–processing inequality and an entropy–contractive observation–level semigroup. Even when the bulk dynamics is law–time reversible, these observation kernels generate a strict one–step dissipation inequality for an observation–level divergence, providing a clean separation between microscopic reversibility and macroscopic arrows of time. The main result is an origin–stabilization theorem: under law–level EVI contractivity the bulk semigroup admits a unique invariant law, and all law–time trajectories converge to this “origin law” at a geometric rate in FBHK–Wasserstein distance. With an additional comparability assumption between FBHK–Wasserstein and total variation metrics, the paper derives a Dobrushin–type bound and adapts Georgii’s one–dimensional Gibbs/DLR argument to show that the stabilized origin law coincides with the unique DLR/Gibbs measure compatible with the one–step specification. Finally, the construction is packaged into a simple category of reversible PFHS interfaces, where origin–preserving endomorphisms give a mathematically controlled notion of self–reference for persistent, law–time–symmetric systems.

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