{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:F4XSQ277GEKCK6WSDSWLJUDM2X","short_pith_number":"pith:F4XSQ277","schema_version":"1.0","canonical_sha256":"2f2f286bff3114257ad21cacb4d06cd5e681088838510923760fe4c4109db6b6","source":{"kind":"arxiv","id":"1105.4965","version":1},"attestation_state":"computed","paper":{"title":"Evolution of scaling emergence in large-scale spatial epidemic spreading","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.SI","physics.data-an","q-bio.PE"],"primary_cat":"physics.soc-ph","authors_text":"Kan Zhang, Lin Wang, Xiang Li, Yan Zhang, Yi-Qing Zhang","submitted_at":"2011-05-25T08:27:37Z","abstract_excerpt":"Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which is still hardly been clarified.\n  Methodology/Principal Findings: In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time b"},"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":"1105.4965","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-25T08:27:37Z","cross_cats_sorted":["cs.SI","physics.data-an","q-bio.PE"],"title_canon_sha256":"eec12fd97b3e1295200424edfdc140f7a94cddb0f323608935a8af4843ee8d74","abstract_canon_sha256":"6e5898e199f8159a75bb6059c82f79a3798ea1fd296ab61b93770ce6a8f6fc2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:20.995596Z","signature_b64":"zVid9hABesDlXYciomL2XZxxUytf4YwKgScY0xzya2RWcYwIVYiph1J6gHJxCNGUW52kAimyJ8KkmBXWvDAwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f2f286bff3114257ad21cacb4d06cd5e681088838510923760fe4c4109db6b6","last_reissued_at":"2026-05-18T04:21:20.995032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:20.995032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Evolution of scaling emergence in large-scale spatial epidemic spreading","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.SI","physics.data-an","q-bio.PE"],"primary_cat":"physics.soc-ph","authors_text":"Kan Zhang, Lin Wang, Xiang Li, Yan Zhang, Yi-Qing Zhang","submitted_at":"2011-05-25T08:27:37Z","abstract_excerpt":"Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which is still hardly been clarified.\n  Methodology/Principal Findings: In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4965","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":""},"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":"1105.4965","created_at":"2026-05-18T04:21:20.995111+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4965v1","created_at":"2026-05-18T04:21:20.995111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4965","created_at":"2026-05-18T04:21:20.995111+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4XSQ277GEKC","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4XSQ277GEKCK6WS","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4XSQ277","created_at":"2026-05-18T12:26:28.662955+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/F4XSQ277GEKCK6WSDSWLJUDM2X","json":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X.json","graph_json":"https://pith.science/api/pith-number/F4XSQ277GEKCK6WSDSWLJUDM2X/graph.json","events_json":"https://pith.science/api/pith-number/F4XSQ277GEKCK6WSDSWLJUDM2X/events.json","paper":"https://pith.science/paper/F4XSQ277"},"agent_actions":{"view_html":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X","download_json":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X.json","view_paper":"https://pith.science/paper/F4XSQ277","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4965&json=true","fetch_graph":"https://pith.science/api/pith-number/F4XSQ277GEKCK6WSDSWLJUDM2X/graph.json","fetch_events":"https://pith.science/api/pith-number/F4XSQ277GEKCK6WSDSWLJUDM2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X/action/storage_attestation","attest_author":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X/action/author_attestation","sign_citation":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X/action/citation_signature","submit_replication":"https://pith.science/pith/F4XSQ277GEKCK6WSDSWLJUDM2X/action/replication_record"}},"created_at":"2026-05-18T04:21:20.995111+00:00","updated_at":"2026-05-18T04:21:20.995111+00:00"}