Atlas Periodic Table v0
Do unrelated dynamical systems organize into families based on the geometry of their behavioral landscapes?
Topic
Regime Geography
A collection of 5 issues
Universality Library v0.1 — Seam Morphology Invariants
Seam morphology invariants separate canonical dynamical systems into recurring topology classes. Using motif-based seam typing and component entropy, we show that forced Duffing produces a percolating boundary mesh, while Hénon and Logistic maps exhibit fragmented seam structures.
Regime Geography as a First-Class Object in Dynamical and Learned Systems
The global behavioral structure of a dynamical system forms a measurable geometric object. We formalize this object as a Regime Geography and define reproducible metrics for constructing and comparing such geographies across systems and model versions
ΔΩ
ΔΩ is a multi-channel metric for measuring structural deformation in regime geography. By separating agreement drift, support erosion, and boundary displacement, Recursion Geometry distinguishes numerical degradation from true model collapse.
Regime Geography as a First-Class Object
Recursion Geometry formalizes regime geography as a first-class object: a deterministic mapping from parameter space to dynamical class. Through versioned atlases and three-channel ΔΩ diagnostics, we shift from trajectory analysis to cartographic science.