{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AUGCZAV2ITE2NH5EZEY5CNXSCN","short_pith_number":"pith:AUGCZAV2","schema_version":"1.0","canonical_sha256":"050c2c82ba44c9a69fa4c931d136f21373da9c19bb20686c1085f9f5367690f1","source":{"kind":"arxiv","id":"1207.0349","version":2},"attestation_state":"computed","paper":{"title":"Fundamental Structural Constraint of Random Scale-Free Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Kim, Hawoong Jeong, Meesoon Ha, Yongjoo Baek","submitted_at":"2012-07-02T11:34:56Z","abstract_excerpt":"We study the structural constraint of random scale-free networks that determines possible combinations of the degree exponent $\\gamma$ and the upper cutoff $k_c$ in the thermodynamic limit. We employ the framework of graphicality transitions proposed by [Del Genio and co-workers, Phys. Rev. Lett. {\\bf 107}, 178701 (2011)], while making it more rigorous and applicable to general values of kc. Using the graphicality criterion, we show that the upper cutoff must be lower than $k_c N^{1/\\gamma}$ for $\\gamma < 2$, whereas any upper cutoff is allowed for $\\gamma > 2$. This result is also numerically"},"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":"1207.0349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-02T11:34:56Z","cross_cats_sorted":["cs.CR","physics.soc-ph"],"title_canon_sha256":"f0019121fa72a3037f4bc53004becb722ed53c7c8825249a043109e94bbf62ac","abstract_canon_sha256":"5d4931fe3d9dde97f0c0b99056a02f400c19cc66d645b4e19debd9e987c0b5b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:08.614588Z","signature_b64":"+g5DkaUTGTYvTZpE/JrvTqEtGCUNm4wTFquehumq9Oeosd+/2VpDeb6AYd94p+b/gheHg+DwpNRnR2mNTQ4LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"050c2c82ba44c9a69fa4c931d136f21373da9c19bb20686c1085f9f5367690f1","last_reissued_at":"2026-05-18T02:21:08.613998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:08.613998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fundamental Structural Constraint of Random Scale-Free Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Kim, Hawoong Jeong, Meesoon Ha, Yongjoo Baek","submitted_at":"2012-07-02T11:34:56Z","abstract_excerpt":"We study the structural constraint of random scale-free networks that determines possible combinations of the degree exponent $\\gamma$ and the upper cutoff $k_c$ in the thermodynamic limit. We employ the framework of graphicality transitions proposed by [Del Genio and co-workers, Phys. Rev. Lett. {\\bf 107}, 178701 (2011)], while making it more rigorous and applicable to general values of kc. Using the graphicality criterion, we show that the upper cutoff must be lower than $k_c N^{1/\\gamma}$ for $\\gamma < 2$, whereas any upper cutoff is allowed for $\\gamma > 2$. This result is also numerically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0349","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":"1207.0349","created_at":"2026-05-18T02:21:08.614100+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.0349v2","created_at":"2026-05-18T02:21:08.614100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0349","created_at":"2026-05-18T02:21:08.614100+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUGCZAV2ITE2","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUGCZAV2ITE2NH5E","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUGCZAV2","created_at":"2026-05-18T12:26:58.693483+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/AUGCZAV2ITE2NH5EZEY5CNXSCN","json":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN.json","graph_json":"https://pith.science/api/pith-number/AUGCZAV2ITE2NH5EZEY5CNXSCN/graph.json","events_json":"https://pith.science/api/pith-number/AUGCZAV2ITE2NH5EZEY5CNXSCN/events.json","paper":"https://pith.science/paper/AUGCZAV2"},"agent_actions":{"view_html":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN","download_json":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN.json","view_paper":"https://pith.science/paper/AUGCZAV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.0349&json=true","fetch_graph":"https://pith.science/api/pith-number/AUGCZAV2ITE2NH5EZEY5CNXSCN/graph.json","fetch_events":"https://pith.science/api/pith-number/AUGCZAV2ITE2NH5EZEY5CNXSCN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN/action/storage_attestation","attest_author":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN/action/author_attestation","sign_citation":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN/action/citation_signature","submit_replication":"https://pith.science/pith/AUGCZAV2ITE2NH5EZEY5CNXSCN/action/replication_record"}},"created_at":"2026-05-18T02:21:08.614100+00:00","updated_at":"2026-05-18T02:21:08.614100+00:00"}