{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MG7MKJZYZ33EYKV4DC4PUPHOL2","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":"1d7299fc99a65e96d988795522f5193ab1bc2a34be279ad1695cb08538a6bdd1","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-04-20T15:15:06Z","title_canon_sha256":"54d08ea1c7593b88ddb4750d79d6ebe9c96bd872db447e7f37e623f29a46f199"},"schema_version":"1.0","source":{"id":"1904.09457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09457","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09457v1","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09457","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"MG7MKJZYZ33E","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MG7MKJZYZ33EYKV4","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MG7MKJZY","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:c98df7e9452d026cb003dddf1dfe3827db0d27ac07baae8e39de7d03d5c05602","target":"graph","created_at":"2026-05-17T23:40:38Z","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":"Due to their conceptual and mathematical simplicity, Erd\\\"os-R\\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely considered in complex network theory, the condensation of degrees has hitherto eluded a careful study. Here we show that the degree statistics of the classical random graph model undergoes a first-order phase transition between a Poisson-like distribution and a condensed phase, the latter characterized by a large fraction of nodes having degrees in a limited sector","authors_text":"Fernando L. Metz, Isaac P\\'erez Castillo","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-04-20T15:15:06Z","title":"Condensation of degrees emerging through a first-order phase transition in classical random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09457","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:ada792aceb202cf0963fe82a663291ef7ed5c142bea1a3aad2592497e45326f4","target":"record","created_at":"2026-05-17T23:40:38Z","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":"1d7299fc99a65e96d988795522f5193ab1bc2a34be279ad1695cb08538a6bdd1","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-04-20T15:15:06Z","title_canon_sha256":"54d08ea1c7593b88ddb4750d79d6ebe9c96bd872db447e7f37e623f29a46f199"},"schema_version":"1.0","source":{"id":"1904.09457","kind":"arxiv","version":1}},"canonical_sha256":"61bec52738cef64c2abc18b8fa3cee5ea90dd7f061d66d636606dc521ea79d34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61bec52738cef64c2abc18b8fa3cee5ea90dd7f061d66d636606dc521ea79d34","first_computed_at":"2026-05-17T23:40:38.828155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:38.828155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nitkfKtMBr92O8iENNsry3sVvxl6JAQv77gj6uX1/UcbyXRmY3z+CZZnTcvc1Le3JrOm5dnzd0F71vUy3aswDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:38.828632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ada792aceb202cf0963fe82a663291ef7ed5c142bea1a3aad2592497e45326f4","sha256:c98df7e9452d026cb003dddf1dfe3827db0d27ac07baae8e39de7d03d5c05602"],"state_sha256":"9b4cec0e600881ce54d2cc75a75dfa94a637b0e9bc2e4a24f700c5fae9fcb546"}