{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7THTOKRLQMSKZYC547O4DHPPRJ","short_pith_number":"pith:7THTOKRL","schema_version":"1.0","canonical_sha256":"fccf372a2b8324ace05de7ddc19def8a6f7b33b7cc6b93ee469f95413e1ba1ab","source":{"kind":"arxiv","id":"1103.0765","version":1},"attestation_state":"computed","paper":{"title":"Watersheds and Explosive percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hans J. Herrmann, Nuno A. M. Araujo","submitted_at":"2011-03-03T19:44:23Z","abstract_excerpt":"The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, "},"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":"1103.0765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-03T19:44:23Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"8dbdae58bae963ef9fb8d8d9808673803113b38ba28b411479367d7510e394f3","abstract_canon_sha256":"fe19ce7501b85855fffa67990eb176a34a2cd8f0950de863f9a6e7da050bca86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:42.042125Z","signature_b64":"cLCjGbeuGcsGBVKpEldp98iI0BZbGAsTlXd+uPpYe6XAqFZTubSIdTuAgj6o84PdNeL1fG0o4208lkYAnBMYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fccf372a2b8324ace05de7ddc19def8a6f7b33b7cc6b93ee469f95413e1ba1ab","last_reissued_at":"2026-05-18T04:16:42.041424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:42.041424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Watersheds and Explosive percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hans J. Herrmann, Nuno A. M. Araujo","submitted_at":"2011-03-03T19:44:23Z","abstract_excerpt":"The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0765","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":"1103.0765","created_at":"2026-05-18T04:16:42.041541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.0765v1","created_at":"2026-05-18T04:16:42.041541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0765","created_at":"2026-05-18T04:16:42.041541+00:00"},{"alias_kind":"pith_short_12","alias_value":"7THTOKRLQMSK","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7THTOKRLQMSKZYC5","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7THTOKRL","created_at":"2026-05-18T12:26:22.705136+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/7THTOKRLQMSKZYC547O4DHPPRJ","json":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ.json","graph_json":"https://pith.science/api/pith-number/7THTOKRLQMSKZYC547O4DHPPRJ/graph.json","events_json":"https://pith.science/api/pith-number/7THTOKRLQMSKZYC547O4DHPPRJ/events.json","paper":"https://pith.science/paper/7THTOKRL"},"agent_actions":{"view_html":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ","download_json":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ.json","view_paper":"https://pith.science/paper/7THTOKRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.0765&json=true","fetch_graph":"https://pith.science/api/pith-number/7THTOKRLQMSKZYC547O4DHPPRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7THTOKRLQMSKZYC547O4DHPPRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ/action/storage_attestation","attest_author":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ/action/author_attestation","sign_citation":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ/action/citation_signature","submit_replication":"https://pith.science/pith/7THTOKRLQMSKZYC547O4DHPPRJ/action/replication_record"}},"created_at":"2026-05-18T04:16:42.041541+00:00","updated_at":"2026-05-18T04:16:42.041541+00:00"}