{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X4RQBCIEIYN3V6TIN3CVHRHVKU","short_pith_number":"pith:X4RQBCIE","canonical_record":{"source":{"id":"1405.0388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-02T12:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"8c027497e923a7a659efba4980d76123c9b70945b97781e9f13c33529ca356ea","abstract_canon_sha256":"1725447db4c78f3b3ef1d7cce09758aae0914c3cdc7f70da2511ff70bc7292fa"},"schema_version":"1.0"},"canonical_sha256":"bf23008904461bbafa686ec553c4f555038607744284650f55b9d86757900459","source":{"kind":"arxiv","id":"1405.0388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0388","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0388v1","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0388","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"X4RQBCIEIYN3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X4RQBCIEIYN3V6TI","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X4RQBCIE","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X4RQBCIEIYN3V6TIN3CVHRHVKU","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-02T12:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"8c027497e923a7a659efba4980d76123c9b70945b97781e9f13c33529ca356ea","abstract_canon_sha256":"1725447db4c78f3b3ef1d7cce09758aae0914c3cdc7f70da2511ff70bc7292fa"},"schema_version":"1.0"},"canonical_sha256":"bf23008904461bbafa686ec553c4f555038607744284650f55b9d86757900459","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:40.652955Z","signature_b64":"WBC8W/IcvVuuvsjpNklwFWUDlKn3krWmGjJAM19qM+xftZSqd7mN7OxGID1dVpBhFoP0FHYsIo1YZMLqZwxBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf23008904461bbafa686ec553c4f555038607744284650f55b9d86757900459","last_reissued_at":"2026-05-18T02:28:40.652481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:40.652481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0388","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ni++ecJdRKDD4CmKil9fHWNJD5PkxFwbrE+rDrCYyJ99l20jAQkrM3SEEiKfexm4A7ScJeW8pDHpMO0WH9hJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:38:41.397490Z"},"content_sha256":"6b6a7eba659f2482a6f15f55a724e737fd4d6dc3799ec79bb70747d5eabfad3b","schema_version":"1.0","event_id":"sha256:6b6a7eba659f2482a6f15f55a724e737fd4d6dc3799ec79bb70747d5eabfad3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X4RQBCIEIYN3V6TIN3CVHRHVKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explosive Percolation: Unusual Transitions of a Simple Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kosmas Kosmidis, Michael Maragakis, Nikolaos Bastas, Paraskevas Giazitzidis","submitted_at":"2014-05-02T12:03:37Z","abstract_excerpt":"In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation process so that the emergence of the spanning cluster is delayed. This slight modification turns out to have a great impact on the percolation phase transition. The resulting transition is so sharp that it was termed explosive, and it was at first considered to be discontinuous. This surprising fact stimulated considerable interest in \"Achlioptas processes\". La"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0388","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1j4cPjug2ejcf3PcEIEU5l7OFde9cSRDLrAwtp/R6Y1G7yZbHrjy6Q2eINlaInfbDHlH7Bso75XQlDpO94VsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:38:41.398201Z"},"content_sha256":"6f814d08539ca0b4765038e159a8ff5ec1c502c1a7761b461746c13fee5109a5","schema_version":"1.0","event_id":"sha256:6f814d08539ca0b4765038e159a8ff5ec1c502c1a7761b461746c13fee5109a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/bundle.json","state_url":"https://pith.science/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T10:38:41Z","links":{"resolver":"https://pith.science/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU","bundle":"https://pith.science/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/bundle.json","state":"https://pith.science/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4RQBCIEIYN3V6TIN3CVHRHVKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X4RQBCIEIYN3V6TIN3CVHRHVKU","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":"1725447db4c78f3b3ef1d7cce09758aae0914c3cdc7f70da2511ff70bc7292fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-02T12:03:37Z","title_canon_sha256":"8c027497e923a7a659efba4980d76123c9b70945b97781e9f13c33529ca356ea"},"schema_version":"1.0","source":{"id":"1405.0388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0388","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0388v1","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0388","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"X4RQBCIEIYN3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X4RQBCIEIYN3V6TI","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X4RQBCIE","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:6f814d08539ca0b4765038e159a8ff5ec1c502c1a7761b461746c13fee5109a5","target":"graph","created_at":"2026-05-18T02:28:40Z","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 paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation process so that the emergence of the spanning cluster is delayed. This slight modification turns out to have a great impact on the percolation phase transition. The resulting transition is so sharp that it was termed explosive, and it was at first considered to be discontinuous. This surprising fact stimulated considerable interest in \"Achlioptas processes\". La","authors_text":"Kosmas Kosmidis, Michael Maragakis, Nikolaos Bastas, Paraskevas Giazitzidis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-02T12:03:37Z","title":"Explosive Percolation: Unusual Transitions of a Simple Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0388","kind":"arxiv","version":1},"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":"sha256:6b6a7eba659f2482a6f15f55a724e737fd4d6dc3799ec79bb70747d5eabfad3b","target":"record","created_at":"2026-05-18T02:28:40Z","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":"1725447db4c78f3b3ef1d7cce09758aae0914c3cdc7f70da2511ff70bc7292fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-02T12:03:37Z","title_canon_sha256":"8c027497e923a7a659efba4980d76123c9b70945b97781e9f13c33529ca356ea"},"schema_version":"1.0","source":{"id":"1405.0388","kind":"arxiv","version":1}},"canonical_sha256":"bf23008904461bbafa686ec553c4f555038607744284650f55b9d86757900459","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf23008904461bbafa686ec553c4f555038607744284650f55b9d86757900459","first_computed_at":"2026-05-18T02:28:40.652481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:40.652481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBC8W/IcvVuuvsjpNklwFWUDlKn3krWmGjJAM19qM+xftZSqd7mN7OxGID1dVpBhFoP0FHYsIo1YZMLqZwxBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:40.652955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6a7eba659f2482a6f15f55a724e737fd4d6dc3799ec79bb70747d5eabfad3b","sha256:6f814d08539ca0b4765038e159a8ff5ec1c502c1a7761b461746c13fee5109a5"],"state_sha256":"1e7ce3c88d3d41f0d4705c8580f407976540fbdd8fe695cbb3621698839721d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRr/Zm7RI8wbMuJMbX+vcjT4qPmG+LE3u13fTbPWZyh4l9q/cz16C3lTOQ8fNDJTa+m5cTStB9XhiXykJ8jYDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:38:41.402081Z","bundle_sha256":"6c7abc627a6216618230324faaf60ba0881164c7d7b5d8c32500f796e0d935d3"}}