{"paper":{"title":"Entropic Collapse and Extreme First-Passage Times in Discrete Ballistic Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"On hierarchical networks, minimum arrival times of many walkers follow a discrete distribution with a strict lower bound set by the graph, rather than any classical extreme-value law.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bhargav R. Karamched","submitted_at":"2026-01-07T06:04:57Z","abstract_excerpt":"We investigate the extreme first-passage statistics of $N$ non-interacting random walkers on discrete, hierarchical networks. {By distinguishing between transport limited by escape from localized initial states (injection-limited) and transport limited by the extended network (bulk-limited), we identify a class of extreme value statistics that arises in geometries dominated by source traps (e.g., the Comet graph).} In this regime, the distribution of the minimum arrival time does not converge to any of the classical generalized extreme value distributions. Instead, it follows a discrete distri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the distribution of the minimum arrival time does not converge to any of the classical generalized extreme value distributions. Instead, it follows a discrete distribution with a strict lower time bound determined by the properties of the hierarchical network.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The networks are discrete and hierarchical, walkers are non-interacting, and the transport regime can be cleanly classified as injection-limited versus bulk-limited so that the lower bound and entropic collapse apply as stated.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In injection-limited hierarchical networks, minimum first-passage times of non-interacting walkers follow a discrete distribution with strict lower bound, destroyed by entropic collapse in bulk-limited geometries like the Bethe lattice.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"On hierarchical networks, minimum arrival times of many walkers follow a discrete distribution with a strict lower bound set by the graph, rather than any classical extreme-value law.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2a44aff990abf3e156b43207f5d071167e42d652f22102982bf4c3841914dd68"},"source":{"id":"2601.03622","kind":"arxiv","version":2},"verdict":{"id":"094deab7-5604-46d7-b11d-ebd15865eabd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T17:11:44.634131Z","strongest_claim":"the distribution of the minimum arrival time does not converge to any of the classical generalized extreme value distributions. Instead, it follows a discrete distribution with a strict lower time bound determined by the properties of the hierarchical network.","one_line_summary":"In injection-limited hierarchical networks, minimum first-passage times of non-interacting walkers follow a discrete distribution with strict lower bound, destroyed by entropic collapse in bulk-limited geometries like the Bethe lattice.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The networks are discrete and hierarchical, walkers are non-interacting, and the transport regime can be cleanly classified as injection-limited versus bulk-limited so that the lower bound and entropic collapse apply as stated.","pith_extraction_headline":"On hierarchical networks, minimum arrival times of many walkers follow a discrete distribution with a strict lower bound set by the graph, rather than any classical extreme-value law."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"51a6e80ec9748d61b841ebd066aaa46090af17827992a49ae928a63c411883b3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}