Supplemental Materials (Revision 3) Probabilistic Modeling on Riemannian Manifolds: A Unified Geometric Framework with Novel Stability Guarantees and Curvature-Adaptive Algorithms

Supplemental Materials (Revision 3 – Complete)Probabilistic Modeling on Riemannian Manifolds:A Unified G e ometric F ramework w i th N ovel StabilityGuarantees and Curvature-Adaptive AlgorithmsAnthony L. PerryIndependent Researcher, Hot Springs, Arkansas 71901, [e-mail] — ORCID: 0009-0009-1279-3056April 2026 — Revision 3 vMF sampler – Wood (1994) algorithm, validated against known mean Bingham sampler on S2 – ACG rejection sampler, validatedWishart sampler – corrected Bartlett decomposition, validatedSO3ScoreNet, SPDScoreNet, HyperbolicScoreNet – all implementedNLL estimator – probability-flow ODE with Hutchinson trace EuclideanManifold and PoincareHyperbolic – implemented for Experiment 3 Experiment scripts – all three fully runnable end-to-endChi-squared divergence – proper KDE estimator License and CitationMIT License. Copyright (c) 2026 Anthony L. Perry. Repository: https://doi.org/10.5281/zenodo.18347585 Contact: [e-mail]