{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TKHHUXB7MDXYF5EECP353HHBRY","short_pith_number":"pith:TKHHUXB7","schema_version":"1.0","canonical_sha256":"9a8e7a5c3f60ef82f48413f7dd9ce18e0b380b9ae6efa6b7b90d49213a6621c9","source":{"kind":"arxiv","id":"1109.0940","version":2},"attestation_state":"computed","paper":{"title":"Entropy rate of non-equilibrium growing networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Arda Halu, Ginestra Bianconi, Kun Zhao, Simone Severini","submitted_at":"2011-09-05T15:41:10Z","abstract_excerpt":"New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we define the entropy rate of growing network models. This entropy rate quantifies how many labeled networks are typically generated by the growing network models. We analytically evaluate the difference between the entropy rate of growing tree network models and the entropy of tree networks that have the same asymptotic degree distribution. We find that the gr"},"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":"1109.0940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-09-05T15:41:10Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7af027b6a14cdf5e1c1bb765e1ddcdf1a29cb8517303d9333a6fa0bf8a503b98","abstract_canon_sha256":"3d039ec9999636c704e3da56665da3ad1d046be54ea9bda59b3ceaf2f692a41d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:39.674705Z","signature_b64":"QovmwBxd2h7rf0gLDfZYDOUl0Mv/I5ZsxMwGREghMV0W20V+9Nb910im8VaLNFU9OstZkVUtpqYmoUXX6KIaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a8e7a5c3f60ef82f48413f7dd9ce18e0b380b9ae6efa6b7b90d49213a6621c9","last_reissued_at":"2026-05-18T02:00:39.673957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:39.673957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy rate of non-equilibrium growing networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Arda Halu, Ginestra Bianconi, Kun Zhao, Simone Severini","submitted_at":"2011-09-05T15:41:10Z","abstract_excerpt":"New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we define the entropy rate of growing network models. This entropy rate quantifies how many labeled networks are typically generated by the growing network models. We analytically evaluate the difference between the entropy rate of growing tree network models and the entropy of tree networks that have the same asymptotic degree distribution. We find that the gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0940","kind":"arxiv","version":2},"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":"1109.0940","created_at":"2026-05-18T02:00:39.674063+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0940v2","created_at":"2026-05-18T02:00:39.674063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0940","created_at":"2026-05-18T02:00:39.674063+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKHHUXB7MDXY","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKHHUXB7MDXYF5EE","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKHHUXB7","created_at":"2026-05-18T12:26:42.757692+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/TKHHUXB7MDXYF5EECP353HHBRY","json":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY.json","graph_json":"https://pith.science/api/pith-number/TKHHUXB7MDXYF5EECP353HHBRY/graph.json","events_json":"https://pith.science/api/pith-number/TKHHUXB7MDXYF5EECP353HHBRY/events.json","paper":"https://pith.science/paper/TKHHUXB7"},"agent_actions":{"view_html":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY","download_json":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY.json","view_paper":"https://pith.science/paper/TKHHUXB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0940&json=true","fetch_graph":"https://pith.science/api/pith-number/TKHHUXB7MDXYF5EECP353HHBRY/graph.json","fetch_events":"https://pith.science/api/pith-number/TKHHUXB7MDXYF5EECP353HHBRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY/action/storage_attestation","attest_author":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY/action/author_attestation","sign_citation":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY/action/citation_signature","submit_replication":"https://pith.science/pith/TKHHUXB7MDXYF5EECP353HHBRY/action/replication_record"}},"created_at":"2026-05-18T02:00:39.674063+00:00","updated_at":"2026-05-18T02:00:39.674063+00:00"}