{"paper":{"title":"Traveling Waves and Bumps in $p$-adic NNs]{Pseudo-Traveling Waves and Bumps in Quantum and Classical Hierarchical Cellular Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chayapuntika Indoung, W. A. Z\\'u\\~niga-Galindo; B. A. Zambrano-Luna","submitted_at":"2026-05-18T17:48:41Z","abstract_excerpt":"We study the existence of pseudo-traveling waves and bump solutions for two classes of hierarchical cellular neural networks (CNNs) defined over the ring of $p$-adic integers $\\mathbb{Z}_{p}$. The first type is a $p$-adic CNN described by a reaction-diffusion equation, while the second type is its quantum analog obtained via Wick rotation. The $p$-adic CNNs are hierarchical versions of the classical Chua-Yang CNNs; these networks have a tree-like hierarchical architecture with infinitely many cells and hidden layers. The states are governed by integro-differential equations on $% \\mathbb{Z}_{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18717/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.047501Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b8e228bc9474a7d230dd6b64088775ad459ad5a95efb804eaa41e6030bae8e2e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}