Preprint / scholarly article

Infinite Hierarchical Holographic Observation Quotients

K. Takahashi

Published
DOI
10.5281/zenodo.17684539

Abstract

Mathematically, the core results are modest but explicit: (i) stability of EVI (Evolution Variational Inequality) gradient flows under a truncated ℓ² metric on countable products and inverse limits, (ii) a design-oriented notion of adaptive hierarchical box complexity whose exponent collapses to 0 under mild, uniform small-scale assumptions, and (iii) a depth-independent compute bound for JKO-type numerical implementations when per-level costs form a summable sequence.

Keywords

  • gradient flows
  • holographic observation quotient
  • entropy-transport
  • hellinger-kantorovich
  • bures metric
  • adaptive hierarchical box complexity
  • information theory
  • AI
  • assouad-type dimensions
  • jko scheme

Identifiers and source records