{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2INI22YRXODVDZWKMHBQ47P34H","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":"572d63629a1815b45d2c179a33c6babcc206500b77bbe27e013c33c626683fdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-13T08:31:06Z","title_canon_sha256":"ac08c088da2ebe8367d9c3278288990745dcc58b7483d52783f5f69ffdc7c1c7"},"schema_version":"1.0","source":{"id":"1703.04288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04288","created_at":"2026-05-18T00:42:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04288v1","created_at":"2026-05-18T00:42:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04288","created_at":"2026-05-18T00:42:01Z"},{"alias_kind":"pith_short_12","alias_value":"2INI22YRXODV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2INI22YRXODVDZWK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2INI22YR","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:57ad740a496137c767ad313fe79cce7bb8fb91d22e9a353e3260396a8c184683","target":"graph","created_at":"2026-05-18T00:42:01Z","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":"A two-step contagion model with a single seed serves as a cornerstone for understanding the critical behaviors and underlying mechanism of discontinuous percolation transitions induced by cascade dynamics. When the contagion spreads from a single seed, a cluster of infected and recovered nodes grows without any cluster merging process. However, when the contagion starts from multiple seeds of $O(N)$ where $N$ is the system size, a node weakened by a seed can be infected more easily when it is in contact with another node infected by a different pathogen seed. This contagion process can be view","authors_text":"B. Kahng, Deokjae Lee, Wonjun Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-13T08:31:06Z","title":"Critical behavior of a two-step contagion model with multiple seeds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04288","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:bd2d150a2d0756ca51163baaa6fdd06fdcbc0c888d0cded4b1b9786e4bd3bb6e","target":"record","created_at":"2026-05-18T00:42:01Z","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":"572d63629a1815b45d2c179a33c6babcc206500b77bbe27e013c33c626683fdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-13T08:31:06Z","title_canon_sha256":"ac08c088da2ebe8367d9c3278288990745dcc58b7483d52783f5f69ffdc7c1c7"},"schema_version":"1.0","source":{"id":"1703.04288","kind":"arxiv","version":1}},"canonical_sha256":"d21a8d6b11bb8751e6ca61c30e7dfbe1cb419815a4e124d5ebdada731436a568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d21a8d6b11bb8751e6ca61c30e7dfbe1cb419815a4e124d5ebdada731436a568","first_computed_at":"2026-05-18T00:42:01.547843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:01.547843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QK0u4ilVuev5crdwwPtreQucmojYu+TSJYxye/yVZ6EA/g2jrlF9oHfkoaRUz25LESZxyQ8RPgKHNiA5X4y1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:01.548461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd2d150a2d0756ca51163baaa6fdd06fdcbc0c888d0cded4b1b9786e4bd3bb6e","sha256:57ad740a496137c767ad313fe79cce7bb8fb91d22e9a353e3260396a8c184683"],"state_sha256":"7f8c5dfd6ca4c7fdd2c3c1a08dd44ca3e7dfc8e28d9462262e3756a4cd3e9b15"}