{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YL32RAWOLHIRQRAYBSC3MYHL7G","short_pith_number":"pith:YL32RAWO","schema_version":"1.0","canonical_sha256":"c2f7a882ce59d11844180c85b660ebf9b4140a5dec7fc1442fb7b80e176d55c0","source":{"kind":"arxiv","id":"1210.6259","version":1},"attestation_state":"computed","paper":{"title":"Connectivity of inhomogeneous random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Luc Devroye, Nicolas Fraiman","submitted_at":"2012-10-23T15:03:13Z","abstract_excerpt":"We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a separable metric space, and let their indices form the vertex set of a graph. An edge (i,j) is added with probability min(1, \\K(X_i,X_j) log n/n), where \\K \\ge 0 is a fixed kernel. We show that, under reasonably weak assumptions, the connectivity threshold of the model can be determined."},"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":"1210.6259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-23T15:03:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1805651636c0841a9cbe408ef4933431b9ff4b2ef4f89a51401c3c30460aafb3","abstract_canon_sha256":"c1fc1fed82aef29c10f773f40abd81f1cbe26acaa92ac8e167d9f1dae65fe298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:25.062114Z","signature_b64":"IT/N049xy9zocMN4Idvz49k5Zy2XiNKe780nO/wZBU2wQSb+nvE4nd9C06LQ7kdWFAUCKSwg+fxXVuONfKzDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2f7a882ce59d11844180c85b660ebf9b4140a5dec7fc1442fb7b80e176d55c0","last_reissued_at":"2026-05-18T03:42:25.061621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:25.061621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity of inhomogeneous random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Luc Devroye, Nicolas Fraiman","submitted_at":"2012-10-23T15:03:13Z","abstract_excerpt":"We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a separable metric space, and let their indices form the vertex set of a graph. An edge (i,j) is added with probability min(1, \\K(X_i,X_j) log n/n), where \\K \\ge 0 is a fixed kernel. We show that, under reasonably weak assumptions, the connectivity threshold of the model can be determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6259","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":"1210.6259","created_at":"2026-05-18T03:42:25.061688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6259v1","created_at":"2026-05-18T03:42:25.061688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6259","created_at":"2026-05-18T03:42:25.061688+00:00"},{"alias_kind":"pith_short_12","alias_value":"YL32RAWOLHIR","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"YL32RAWOLHIRQRAY","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"YL32RAWO","created_at":"2026-05-18T12:27:27.928770+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/YL32RAWOLHIRQRAYBSC3MYHL7G","json":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G.json","graph_json":"https://pith.science/api/pith-number/YL32RAWOLHIRQRAYBSC3MYHL7G/graph.json","events_json":"https://pith.science/api/pith-number/YL32RAWOLHIRQRAYBSC3MYHL7G/events.json","paper":"https://pith.science/paper/YL32RAWO"},"agent_actions":{"view_html":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G","download_json":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G.json","view_paper":"https://pith.science/paper/YL32RAWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6259&json=true","fetch_graph":"https://pith.science/api/pith-number/YL32RAWOLHIRQRAYBSC3MYHL7G/graph.json","fetch_events":"https://pith.science/api/pith-number/YL32RAWOLHIRQRAYBSC3MYHL7G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G/action/storage_attestation","attest_author":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G/action/author_attestation","sign_citation":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G/action/citation_signature","submit_replication":"https://pith.science/pith/YL32RAWOLHIRQRAYBSC3MYHL7G/action/replication_record"}},"created_at":"2026-05-18T03:42:25.061688+00:00","updated_at":"2026-05-18T03:42:25.061688+00:00"}