{"paper":{"title":"Emergence of power laws in hierarchical dynamics on multi-level graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A hierarchical queue model with Laplacian fluctuations reproduces the power-law exponent of Italian local train delays.","cross_cats":["physics.app-ph"],"primary_cat":"physics.soc-ph","authors_text":"Armando Bazzani, Gregorio Berselli, Mirko Degli Esposti, Tommaso Rondini","submitted_at":"2025-09-23T08:21:20Z","abstract_excerpt":"Power-law distributions are widely recognized in complex systems physics as indicative of underlying complexity in interaction networks and critical macroscopic behavior. Previous studies, notably those of Newman and others, have emphasized the importance of network structure and dynamics in understanding the emergence of such statistical patterns and predicting extreme events. In this study, we investigate the emergence of power-law behavior in delay distributions within a multi-level hierarchical network of agents governed by simple priority rules. Using railway systems as a case study, we m"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The model accurately reproduces the empirically observed power-law exponent associated with the Italian local train delays.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The stochastic fluctuations in scheduled travel times follow a Laplacian distribution derived from empirical data, which is used to drive the dynamics in the hierarchical network model.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A queue-based model of hierarchical train priorities with stochastic delays generates power-law distributions in local train delays matching empirical Italian data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A hierarchical queue model with Laplacian fluctuations reproduces the power-law exponent of Italian local train delays.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15fd1f81d673b70dbb58d628aac25da258694d9a7fd47da579e64213b87c68f1"},"source":{"id":"2509.18782","kind":"arxiv","version":2},"verdict":{"id":"ea120d93-fcbb-4e0a-9077-902bbf8aaa93","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T14:56:11.311798Z","strongest_claim":"The model accurately reproduces the empirically observed power-law exponent associated with the Italian local train delays.","one_line_summary":"A queue-based model of hierarchical train priorities with stochastic delays generates power-law distributions in local train delays matching empirical Italian data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The stochastic fluctuations in scheduled travel times follow a Laplacian distribution derived from empirical data, which is used to drive the dynamics in the hierarchical network model.","pith_extraction_headline":"A hierarchical queue model with Laplacian fluctuations reproduces the power-law exponent of Italian local train delays."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.18782/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":13,"sample":[{"doi":"10.1007/978-1-4757-5426-1","year":2013,"title":"Springer, New York (2013)","work_id":"fe7aa649-49c1-4f5c-b14d-19be8a3c0292","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Reviews of modern physics 74(1), 47 (2002)","work_id":"c03be55d-0da7-4cd4-95ba-02f8ff45d3c0","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"science 286(5439), 509–512 (1999)","work_id":"e37c96b3-5f74-4c51-a2fa-b63059fc461a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Phys ica A: Statistical 10 Mechanics and its Applications 369(1), 29–70 (2006)","work_id":"6ee23271-2c0c-4c4a-a2b7-ee1bce70cca0","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Cont emporary physics 46(5), 323–351 (2005)","work_id":"5c8cfef1-e4d1-413b-9d9f-1cda6ee99e64","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"99c6fe3462ecaee8073ac3a8d48fe738bc3647ca0ac079e34ab280c0a3c6bfb3","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"de5192c45c8fa1dc1d33ba2ee1dad5c18d264731e03b17009045be7feba10282"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}