Ultrametric Structures and Norm-Based p-Adic Operations for Hierarchical and Robust Information Processing
Year: 2026
Type: article
Abstract: In this article, we propose a non-archimedean framework for information processing based on the arithmetic and geometry of p-adic numbers. Exploiting the ultrametric structure of Qp, we introduce norm-based p-adic operations inspired by classical logical connectives that exhibit strong stability under perturbations. The non-archimedean nature of the p-adic norm induces natural scale separation and clustering properties, leading to robust information encoding and spectral localization. Using p-adic Fourier analysis, we show that hierarchical signals decompose into disjoint frequency bands, enabling multiscale information processing with reduced interference. These results provide a mathematical foundation for robust and hierarchical information architectures, with potential applications in signal processing, error-tolerant computation, and non-classical information systems.
Source: Mathematics
DOI: 10.3390/math14081284
Author: Anselmo Torresblanca-Badillo
Institution: Universidad del Norte
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: Universidad del Norte
OpenAlex ID: W7153977930