{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TKA7WMCYXGTOJRZHPPVYFMKJMG","short_pith_number":"pith:TKA7WMCY","canonical_record":{"source":{"id":"1404.4470","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-17T10:07:18Z","cross_cats_sorted":[],"title_canon_sha256":"0f944126192651679bee01ec0ae82d29442288971bd4d536e66d80713b744b37","abstract_canon_sha256":"d88318b1dc613ea14ddcb70da2f792eeeaa26a3cc039f2a8f6b3fbc3619f2d31"},"schema_version":"1.0"},"canonical_sha256":"9a81fb3058b9a6e4c7277beb82b14961bddc77348af7f0c834b3f6388fee8f3a","source":{"kind":"arxiv","id":"1404.4470","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4470","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4470v4","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4470","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"TKA7WMCYXGTO","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TKA7WMCYXGTOJRZH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TKA7WMCY","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TKA7WMCYXGTOJRZHPPVYFMKJMG","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4470","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-17T10:07:18Z","cross_cats_sorted":[],"title_canon_sha256":"0f944126192651679bee01ec0ae82d29442288971bd4d536e66d80713b744b37","abstract_canon_sha256":"d88318b1dc613ea14ddcb70da2f792eeeaa26a3cc039f2a8f6b3fbc3619f2d31"},"schema_version":"1.0"},"canonical_sha256":"9a81fb3058b9a6e4c7277beb82b14961bddc77348af7f0c834b3f6388fee8f3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:05.849825Z","signature_b64":"I26ImIzoNSwnP/4p4qhmx4QYDyB9/F6cVEI53lyrx6NHDWn8Wkc5W7HbvyMupjPhh/6zN+hnaqfCa8JZRWfcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a81fb3058b9a6e4c7277beb82b14961bddc77348af7f0c834b3f6388fee8f3a","last_reissued_at":"2026-05-18T01:37:05.849192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:05.849192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4470","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHzxorDhcgMa0YPjfscCku06sKlR0j05PQvzQPPcNquiBUnu0DFeJe/nbLbUJo6Btb83SmAjkxcBi8Y1TE25Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:51:32.350047Z"},"content_sha256":"b2ea87c589a1c394cc9a8ff41e01387b3afac50f01dce26ccc7c54351333b08f","schema_version":"1.0","event_id":"sha256:b2ea87c589a1c394cc9a8ff41e01387b3afac50f01dce26ccc7c54351333b08f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TKA7WMCYXGTOJRZHPPVYFMKJMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Kahng, Y. S. Cho","submitted_at":"2014-04-17T10:07:18Z","abstract_excerpt":"Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have revealed that a few models exhibit a discontinuous percolation transition (DPT) in cluster merging processes. Unlike the case of continuous transitions, understanding the nature of discontinuous phase transitions requires a detailed study of the system at hand, which has not been undertaken yet for DPTs. Here we examine the cluster size distribution immediately be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4470","kind":"arxiv","version":4},"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":"2026-05-18T01:37:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jiVIliTKzaZob3QhBFq7TVC0RXQohatSbQg4BC4p62J+JsWNETzCzmeDUX9Pa0XFb1xftKNSm6wZpUW8YWU4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:51:32.350402Z"},"content_sha256":"75842a43ed92054e2b6c7a881d013b123b671a78550e7d72138d31104ad05d92","schema_version":"1.0","event_id":"sha256:75842a43ed92054e2b6c7a881d013b123b671a78550e7d72138d31104ad05d92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/bundle.json","state_url":"https://pith.science/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/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":"2026-05-28T13:51:32Z","links":{"resolver":"https://pith.science/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG","bundle":"https://pith.science/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/bundle.json","state":"https://pith.science/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKA7WMCYXGTOJRZHPPVYFMKJMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TKA7WMCYXGTOJRZHPPVYFMKJMG","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":"d88318b1dc613ea14ddcb70da2f792eeeaa26a3cc039f2a8f6b3fbc3619f2d31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-17T10:07:18Z","title_canon_sha256":"0f944126192651679bee01ec0ae82d29442288971bd4d536e66d80713b744b37"},"schema_version":"1.0","source":{"id":"1404.4470","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4470","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4470v4","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4470","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"TKA7WMCYXGTO","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TKA7WMCYXGTOJRZH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TKA7WMCY","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:75842a43ed92054e2b6c7a881d013b123b671a78550e7d72138d31104ad05d92","target":"graph","created_at":"2026-05-18T01:37:05Z","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":"Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have revealed that a few models exhibit a discontinuous percolation transition (DPT) in cluster merging processes. Unlike the case of continuous transitions, understanding the nature of discontinuous phase transitions requires a detailed study of the system at hand, which has not been undertaken yet for DPTs. Here we examine the cluster size distribution immediately be","authors_text":"B. Kahng, Y. S. Cho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-17T10:07:18Z","title":"Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4470","kind":"arxiv","version":4},"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:b2ea87c589a1c394cc9a8ff41e01387b3afac50f01dce26ccc7c54351333b08f","target":"record","created_at":"2026-05-18T01:37:05Z","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":"d88318b1dc613ea14ddcb70da2f792eeeaa26a3cc039f2a8f6b3fbc3619f2d31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-17T10:07:18Z","title_canon_sha256":"0f944126192651679bee01ec0ae82d29442288971bd4d536e66d80713b744b37"},"schema_version":"1.0","source":{"id":"1404.4470","kind":"arxiv","version":4}},"canonical_sha256":"9a81fb3058b9a6e4c7277beb82b14961bddc77348af7f0c834b3f6388fee8f3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a81fb3058b9a6e4c7277beb82b14961bddc77348af7f0c834b3f6388fee8f3a","first_computed_at":"2026-05-18T01:37:05.849192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:05.849192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I26ImIzoNSwnP/4p4qhmx4QYDyB9/F6cVEI53lyrx6NHDWn8Wkc5W7HbvyMupjPhh/6zN+hnaqfCa8JZRWfcBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:05.849825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4470","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ea87c589a1c394cc9a8ff41e01387b3afac50f01dce26ccc7c54351333b08f","sha256:75842a43ed92054e2b6c7a881d013b123b671a78550e7d72138d31104ad05d92"],"state_sha256":"d2fd2b968242f004a093e4999d89fe1c0642c9242624d6530b0045872f3b2c8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7joHhHX9t2xSd+6TxAu9evM7UzT8Zm+cj3E5sgxPsImYIGAeWlxp63Vc0dMoxnbz3WWJiGh+Ig/r/caddVlCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:51:32.352338Z","bundle_sha256":"63333e83bc36f723d2a3a0963c7676c89de64af419179b954498744494733747"}}