# On the Local Ultrametricity of Finite Metric Data

arXiv: https://arxiv.org/abs/2408.07174 · HTML: https://mlsanity.com/paper/2408.07174/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2024.

## Built on by (most cited first, 2 of 2)

- [p-adic Character Neural Network](https://mlsanity.com/paper/2603.29905/) (2026)
- [p-adic Manifold Learning and Benchmark Tasks from Impartial Games](https://mlsanity.com/paper/2605.04374/) (2026)

## Abstract (arXiv)

New local ultrametricity measures for finite metric data are proposed through the viewpoint that their Vietoris-Rips corners are samples from p-adic Mumford curves endowed with a Radon measure coming from a regular differential 1-form. This is experimentally applied to the iris dataset.