{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J2QZW5T4NOKLYWB2CMSUGUNYAH","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":"de5674cb2197a13575ddec6b24a083c657b55796405c6de1db2d6d71da8822f5","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-28T15:12:32Z","title_canon_sha256":"fd7597e47bf7713b958de1a85fbce600631932a4a0e9203b880192a33d4509ec"},"schema_version":"1.0","source":{"id":"1010.5990","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5990","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5990v3","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5990","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"J2QZW5T4NOKL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J2QZW5T4NOKLYWB2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J2QZW5T4","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:ee1ffe860b82e1224c4f3ae0f8be70f49631411683efe87f4f43133f8d4a97e4","target":"graph","created_at":"2026-05-18T04:01:51Z","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":"In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\\H{o}s-R\\'{e}nyi networks, scale-free networks, and square lattice. In finite system, two well-defined Gaussian-like peaks coexist, and the valley between the two peaks is suppressed with the system size increasing. This finite-size effect always appears in typical first-order phase transition. However, both of the two peaks shift to zero point in a power law manner, which indicates the explosive percolation is c","authors_text":"Da-Ning Shi, Liang Tian","cross_cats":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-28T15:12:32Z","title":"The Nature of Explosive Percolation Phase Transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5990","kind":"arxiv","version":3},"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":"sha256:1e01e467526dcaf2f5f2e51f6b2b1a57a141bc21497247c3355092d56358d323","target":"record","created_at":"2026-05-18T04:01:51Z","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":"de5674cb2197a13575ddec6b24a083c657b55796405c6de1db2d6d71da8822f5","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-28T15:12:32Z","title_canon_sha256":"fd7597e47bf7713b958de1a85fbce600631932a4a0e9203b880192a33d4509ec"},"schema_version":"1.0","source":{"id":"1010.5990","kind":"arxiv","version":3}},"canonical_sha256":"4ea19b767c6b94bc583a13254351b801c3cf3a275839fb3afc8ffd83d710ab3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ea19b767c6b94bc583a13254351b801c3cf3a275839fb3afc8ffd83d710ab3c","first_computed_at":"2026-05-18T04:01:51.210194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:51.210194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq6nVxWUUSm32/clh3JKXPUw8HXGTr4sVlBuPLHx79DjMPU9c7XasdH5GAQCj9ppLLBNm78Ckz3T2387YnUWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:51.211060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5990","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e01e467526dcaf2f5f2e51f6b2b1a57a141bc21497247c3355092d56358d323","sha256:ee1ffe860b82e1224c4f3ae0f8be70f49631411683efe87f4f43133f8d4a97e4"],"state_sha256":"1f32630bb200912764fa2d3afcbefab8808bd8959729afe15e091e778620c127"}