{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FM437JNU5H6BWU5BCLOPEZIFXN","short_pith_number":"pith:FM437JNU","schema_version":"1.0","canonical_sha256":"2b39bfa5b4e9fc1b53a112dcf26505bb666ea86c695d823650e22d268286c27b","source":{"kind":"arxiv","id":"1203.0299","version":2},"attestation_state":"computed","paper":{"title":"Criticality and Continuity of Explosive Site Percolation in Random Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nucl-th"],"primary_cat":"physics.soc-ph","authors_text":"D. D. Han, J. H. Qian, Y. G. Ma","submitted_at":"2012-03-01T15:14:42Z","abstract_excerpt":"This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\\\"{o}s and R\\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordina"},"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":"1203.0299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-03-01T15:14:42Z","cross_cats_sorted":["cond-mat.stat-mech","nucl-th"],"title_canon_sha256":"91dc5e05c5e3c2d3ce468594364c5a2bca882ad12c3e24107d4376b62b56a1e1","abstract_canon_sha256":"1605b747141a657d6d7901dd7e27b4c970da378785406c284143c88ebfca6b70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:16.560924Z","signature_b64":"JfBRtOVzpHbEN+Sy3AQYYK5aPrOBH9ubpRdMYoOl55zH11xZssd3cKoFFBv4+/YgZCrpk8L2h7CB2HB/AO9lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b39bfa5b4e9fc1b53a112dcf26505bb666ea86c695d823650e22d268286c27b","last_reissued_at":"2026-05-18T03:39:16.560370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:16.560370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Criticality and Continuity of Explosive Site Percolation in Random Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nucl-th"],"primary_cat":"physics.soc-ph","authors_text":"D. D. Han, J. H. Qian, Y. G. Ma","submitted_at":"2012-03-01T15:14:42Z","abstract_excerpt":"This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\\\"{o}s and R\\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0299","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":"1203.0299","created_at":"2026-05-18T03:39:16.560462+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.0299v2","created_at":"2026-05-18T03:39:16.560462+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0299","created_at":"2026-05-18T03:39:16.560462+00:00"},{"alias_kind":"pith_short_12","alias_value":"FM437JNU5H6B","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FM437JNU5H6BWU5B","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FM437JNU","created_at":"2026-05-18T12:27:06.952714+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/FM437JNU5H6BWU5BCLOPEZIFXN","json":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN.json","graph_json":"https://pith.science/api/pith-number/FM437JNU5H6BWU5BCLOPEZIFXN/graph.json","events_json":"https://pith.science/api/pith-number/FM437JNU5H6BWU5BCLOPEZIFXN/events.json","paper":"https://pith.science/paper/FM437JNU"},"agent_actions":{"view_html":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN","download_json":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN.json","view_paper":"https://pith.science/paper/FM437JNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.0299&json=true","fetch_graph":"https://pith.science/api/pith-number/FM437JNU5H6BWU5BCLOPEZIFXN/graph.json","fetch_events":"https://pith.science/api/pith-number/FM437JNU5H6BWU5BCLOPEZIFXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN/action/storage_attestation","attest_author":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN/action/author_attestation","sign_citation":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN/action/citation_signature","submit_replication":"https://pith.science/pith/FM437JNU5H6BWU5BCLOPEZIFXN/action/replication_record"}},"created_at":"2026-05-18T03:39:16.560462+00:00","updated_at":"2026-05-18T03:39:16.560462+00:00"}