{"paper":{"title":"Urn Modeling of Random Graphs Across Granularity Scales: A Framework for Origin-Destination Human Mobility Networks","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"David Lambert, Fabio Vanni","submitted_at":"2025-08-25T22:38:52Z","abstract_excerpt":"We model human mobility as a combinatorial allocation process, treating trips as distinguishable balls assigned to location-bins and generating origin-destination (OD) networks. From this analogy, we construct a unified three-scale framework, enumerative, probabilistic, and continuum graphon ensembles, and prove a renormalization theorem showing that, in the large sparse regime, these representations converge to a universal mixed-Poisson law. The framework yields compact formulas for key mobility observables, including destination occupancy, vacancy of unvisited sites, coverage (a stopping-tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18544","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/2508.18544/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"}