{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PN7WJBNUAS7W33OB2VAAXHSC6X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3c0ca9bf4ee698da6f83518c2e13606140360d06435c63d574332a2e18d74b18","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"stat.AP","submitted_at":"2012-04-11T11:52:26Z","title_canon_sha256":"77520c69a6eebca23074588f908345daf8902d81f46da92ab16da5f4b3a13840"},"schema_version":"1.0","source":{"id":"1204.2422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2422","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2422v1","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2422","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"PN7WJBNUAS7W","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PN7WJBNUAS7W33OB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PN7WJBNU","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:55d489c299564eef2761c77bd501285b5f577d73a025b67a43b739ada550d7e1","target":"graph","created_at":"2026-05-18T01:57:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"On the basis of dynamical principles we derive the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logist","authors_text":"A. Hernando, A. Plastino","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"stat.AP","submitted_at":"2012-04-11T11:52:26Z","title":"Scale-invariance underlying the logistic equation and its social applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2422","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:342fc2b6e165ba241a8061a37909ff2dc2074a3bc255d19885606cfdda6754b8","target":"record","created_at":"2026-05-18T01:57:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3c0ca9bf4ee698da6f83518c2e13606140360d06435c63d574332a2e18d74b18","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"stat.AP","submitted_at":"2012-04-11T11:52:26Z","title_canon_sha256":"77520c69a6eebca23074588f908345daf8902d81f46da92ab16da5f4b3a13840"},"schema_version":"1.0","source":{"id":"1204.2422","kind":"arxiv","version":1}},"canonical_sha256":"7b7f6485b404bf6dedc1d5400b9e42f5c620ca9b910aa06fc6496e8013518f07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7f6485b404bf6dedc1d5400b9e42f5c620ca9b910aa06fc6496e8013518f07","first_computed_at":"2026-05-18T01:57:53.594306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:53.594306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p76IWpMZRqDD3LA/77xTNdBGP5g0NKxyHZkMnuor82nAr6XM7Vufe0bS68Cdy3fo1vVo/+ccCBlzowWem77vBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:53.595020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342fc2b6e165ba241a8061a37909ff2dc2074a3bc255d19885606cfdda6754b8","sha256:55d489c299564eef2761c77bd501285b5f577d73a025b67a43b739ada550d7e1"],"state_sha256":"a4a4d3bc29b3262c01f3dbb7510c50a758251fca15548717a50cc3ae81cc7023"}