{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:QKDDJHAT2SHCCRBNUQIUI2LCCR","short_pith_number":"pith:QKDDJHAT","schema_version":"1.0","canonical_sha256":"8286349c13d48e21442da4114469621456a337d29ac010a1558f5480bbac017c","source":{"kind":"arxiv","id":"cond-mat/0604069","version":1},"attestation_state":"computed","paper":{"title":"Exact solutions for models of evolving networks with addition and deletion of nodes","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Cristopher Moore, Gourab Ghoshal, M. E. J. Newman","submitted_at":"2006-04-04T19:18:00Z","abstract_excerpt":"There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment -- in which newly appearing vertices attach to previously"},"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":"cond-mat/0604069","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-04-04T19:18:00Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"ad6b5ee6a7d762c80905a201ce7ae2d3da0cb537bd53d9af383a34ac39ee8159","abstract_canon_sha256":"d62de1e10c4e13eafaa811f0bd5f1b61d2148209173fdcf01142f51f09dab41f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:03.187031Z","signature_b64":"95xcHr0iVpbN6f/gkeP1aY+CRTj76HoZFZVfxUq/utCYlNX2Dwt6m6XrsUHylcGl0VjY7EacHxc9nTGQiuiQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8286349c13d48e21442da4114469621456a337d29ac010a1558f5480bbac017c","last_reissued_at":"2026-05-18T04:09:03.186245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:03.186245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solutions for models of evolving networks with addition and deletion of nodes","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Cristopher Moore, Gourab Ghoshal, M. E. J. Newman","submitted_at":"2006-04-04T19:18:00Z","abstract_excerpt":"There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment -- in which newly appearing vertices attach to previously"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0604069","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":"cond-mat/0604069","created_at":"2026-05-18T04:09:03.186579+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0604069v1","created_at":"2026-05-18T04:09:03.186579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0604069","created_at":"2026-05-18T04:09:03.186579+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKDDJHAT2SHC","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKDDJHAT2SHCCRBN","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKDDJHAT","created_at":"2026-05-18T12:25:54.717736+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/QKDDJHAT2SHCCRBNUQIUI2LCCR","json":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR.json","graph_json":"https://pith.science/api/pith-number/QKDDJHAT2SHCCRBNUQIUI2LCCR/graph.json","events_json":"https://pith.science/api/pith-number/QKDDJHAT2SHCCRBNUQIUI2LCCR/events.json","paper":"https://pith.science/paper/QKDDJHAT"},"agent_actions":{"view_html":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR","download_json":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR.json","view_paper":"https://pith.science/paper/QKDDJHAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0604069&json=true","fetch_graph":"https://pith.science/api/pith-number/QKDDJHAT2SHCCRBNUQIUI2LCCR/graph.json","fetch_events":"https://pith.science/api/pith-number/QKDDJHAT2SHCCRBNUQIUI2LCCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR/action/storage_attestation","attest_author":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR/action/author_attestation","sign_citation":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR/action/citation_signature","submit_replication":"https://pith.science/pith/QKDDJHAT2SHCCRBNUQIUI2LCCR/action/replication_record"}},"created_at":"2026-05-18T04:09:03.186579+00:00","updated_at":"2026-05-18T04:09:03.186579+00:00"}