{"paper":{"title":"The Exploratory Study on the Relationship Between the Failure of Distance Metrics in High-Dimensional Space and Emergent Phenomena","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","nlin.AO"],"primary_cat":"cs.IT","authors_text":"Hongzheng Liu, YiNuo Tian, Zhiyue Wu","submitted_at":"2025-04-09T02:19:58Z","abstract_excerpt":"This paper presents a unified framework, integrating information theory and statistical mechanics, to connect metric failure in high-dimensional data with emergence in complex systems. We propose the \"Information Dilution Theorem,\" demonstrating that as dimensionality ($d$) increases, the mutual information efficiency between geometric metrics (e.g., Euclidean distance) and system states decays approximately as $O(1/d)$. This decay arises from the mismatch between linearly growing system entropy and sublinearly growing metric entropy, explaining the mechanism behind distance concentration. Bui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.08807","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/2504.08807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}