{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:WOHH7O2U3OH2H2I2QKG5QLNU47","short_pith_number":"pith:WOHH7O2U","schema_version":"1.0","canonical_sha256":"b38e7fbb54db8fa3e91a828dd82db4e7ec062efcb6372dd2d6ff896ca2d78ac2","source":{"kind":"arxiv","id":"2002.09770","version":5},"attestation_state":"computed","paper":{"title":"Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"A. J. Reagan, C. M. Danforth, D. R. Dewhurst, J. L. Adams, J. R. Minot, M. R. Frank, M. V. Arnold, P. S. Dodds, T. Alshaabi, T. J. Gray","submitted_at":"2020-02-22T20:58:06Z","abstract_excerpt":"Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2002.09770","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2020-02-22T20:58:06Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"a664731b5074981505851093117f9f9070a4f2adb8b4729b8da953db36220378","abstract_canon_sha256":"d0cc426a0e1a8840be252b23aaeec5df7672ac8eec48edf3ea1ae2f310d644cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:37:45.891852Z","signature_b64":"XoYp9RYqem+gqcDVanqe+j7SdfR+dnYpHfRc8Ef2LQ2CfpRDW/pnwY5A+zFGTi3SiYvqaamvqmA4EdH1N10pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b38e7fbb54db8fa3e91a828dd82db4e7ec062efcb6372dd2d6ff896ca2d78ac2","last_reissued_at":"2026-07-05T06:37:45.891368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:37:45.891368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"A. J. Reagan, C. M. Danforth, D. R. Dewhurst, J. L. Adams, J. R. Minot, M. R. Frank, M. V. Arnold, P. S. Dodds, T. Alshaabi, T. J. Gray","submitted_at":"2020-02-22T20:58:06Z","abstract_excerpt":"Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09770","kind":"arxiv","version":5},"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/2002.09770/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2002.09770","created_at":"2026-07-05T06:37:45.891424+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.09770v5","created_at":"2026-07-05T06:37:45.891424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09770","created_at":"2026-07-05T06:37:45.891424+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOHH7O2U3OH2","created_at":"2026-07-05T06:37:45.891424+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOHH7O2U3OH2H2I2","created_at":"2026-07-05T06:37:45.891424+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOHH7O2U","created_at":"2026-07-05T06:37:45.891424+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47","json":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47.json","graph_json":"https://pith.science/api/pith-number/WOHH7O2U3OH2H2I2QKG5QLNU47/graph.json","events_json":"https://pith.science/api/pith-number/WOHH7O2U3OH2H2I2QKG5QLNU47/events.json","paper":"https://pith.science/paper/WOHH7O2U"},"agent_actions":{"view_html":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47","download_json":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47.json","view_paper":"https://pith.science/paper/WOHH7O2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.09770&json=true","fetch_graph":"https://pith.science/api/pith-number/WOHH7O2U3OH2H2I2QKG5QLNU47/graph.json","fetch_events":"https://pith.science/api/pith-number/WOHH7O2U3OH2H2I2QKG5QLNU47/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47/action/storage_attestation","attest_author":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47/action/author_attestation","sign_citation":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47/action/citation_signature","submit_replication":"https://pith.science/pith/WOHH7O2U3OH2H2I2QKG5QLNU47/action/replication_record"}},"created_at":"2026-07-05T06:37:45.891424+00:00","updated_at":"2026-07-05T06:37:45.891424+00:00"}