{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:247WFRFMGP7QAL2YR7HJZBHK66","short_pith_number":"pith:247WFRFM","canonical_record":{"source":{"id":"1606.02739","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-06-08T20:25:04Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"0cfdd9376845bf022d7a28c272b2570fdacf506128f67fb97fbeaf5062d7e52a","abstract_canon_sha256":"368c6586978236a718895a5a81859b4a4121aeb87f7779505271f8013dd46dfb"},"schema_version":"1.0"},"canonical_sha256":"d73f62c4ac33ff002f588fce9c84eaf7846d186c77d3e0ca3d53fd9f412df367","source":{"kind":"arxiv","id":"1606.02739","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02739","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02739v3","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02739","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"pith_short_12","alias_value":"247WFRFMGP7Q","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"247WFRFMGP7QAL2Y","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"247WFRFM","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:247WFRFMGP7QAL2YR7HJZBHK66","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02739","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-06-08T20:25:04Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"0cfdd9376845bf022d7a28c272b2570fdacf506128f67fb97fbeaf5062d7e52a","abstract_canon_sha256":"368c6586978236a718895a5a81859b4a4121aeb87f7779505271f8013dd46dfb"},"schema_version":"1.0"},"canonical_sha256":"d73f62c4ac33ff002f588fce9c84eaf7846d186c77d3e0ca3d53fd9f412df367","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:42.684123Z","signature_b64":"gc62t73kWudfPOSjj8L7PoJzFljWJI44L0UobNhcy2nGb4wep3kZjHRQOoepQ3z0LPliokljo9/4I185GyDZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d73f62c4ac33ff002f588fce9c84eaf7846d186c77d3e0ca3d53fd9f412df367","last_reissued_at":"2026-05-18T00:48:42.683694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:42.683694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02739","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ys5942CS8clnamMuYcSm42HHBLHh1feQN5JcIwFrYP6M7mlPFZBsZZMBVwvLO7a9sZcAPslWLRj99GHi4X4sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:13:18.721271Z"},"content_sha256":"9718aeee7492a8d311425aac8d73a905823a8ac349b986a555569ac9089c7a1c","schema_version":"1.0","event_id":"sha256:9718aeee7492a8d311425aac8d73a905823a8ac349b986a555569ac9089c7a1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:247WFRFMGP7QAL2YR7HJZBHK66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient collective influence maximization in cascading processes with first-order transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Flaviano Morone, Hern\\'an A. Makse, Jeffrey Shaman, Sen Pei, Xian Teng","submitted_at":"2016-06-08T20:25:04Z","abstract_excerpt":"In social networks, the collective behavior of large populations can be shaped by a small set of influencers through a cascading process induced by \"peer pressure\". For large-scale networks, efficient identification of multiple influential spreaders with a linear algorithm in threshold models that exhibit a first-order transition still remains a challenging task. Here we address this issue by exploring the collective influence in general threshold models of behavior cascading. Our analysis reveals that the importance of spreaders is fixed by the subcritical paths along which cascades propagate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02739","kind":"arxiv","version":3},"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":"2026-05-18T00:48:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6k64jcuLBtjB7eBR0Ww8V9sfaP7e56fQhXCJZoE00luFfyyaLD4/3LgYG02adLlT3V5IRkOhFUPZlUDr5uO6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:13:18.721631Z"},"content_sha256":"d0f1d091bd94753175c4f2b11aee571dca1e1cac6c78bd817352a3ac5ebcb0b4","schema_version":"1.0","event_id":"sha256:d0f1d091bd94753175c4f2b11aee571dca1e1cac6c78bd817352a3ac5ebcb0b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/247WFRFMGP7QAL2YR7HJZBHK66/bundle.json","state_url":"https://pith.science/pith/247WFRFMGP7QAL2YR7HJZBHK66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/247WFRFMGP7QAL2YR7HJZBHK66/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":"2026-06-20T06:13:18Z","links":{"resolver":"https://pith.science/pith/247WFRFMGP7QAL2YR7HJZBHK66","bundle":"https://pith.science/pith/247WFRFMGP7QAL2YR7HJZBHK66/bundle.json","state":"https://pith.science/pith/247WFRFMGP7QAL2YR7HJZBHK66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/247WFRFMGP7QAL2YR7HJZBHK66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:247WFRFMGP7QAL2YR7HJZBHK66","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":"368c6586978236a718895a5a81859b4a4121aeb87f7779505271f8013dd46dfb","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-06-08T20:25:04Z","title_canon_sha256":"0cfdd9376845bf022d7a28c272b2570fdacf506128f67fb97fbeaf5062d7e52a"},"schema_version":"1.0","source":{"id":"1606.02739","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02739","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02739v3","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02739","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"pith_short_12","alias_value":"247WFRFMGP7Q","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"247WFRFMGP7QAL2Y","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"247WFRFM","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:d0f1d091bd94753175c4f2b11aee571dca1e1cac6c78bd817352a3ac5ebcb0b4","target":"graph","created_at":"2026-05-18T00:48:42Z","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 social networks, the collective behavior of large populations can be shaped by a small set of influencers through a cascading process induced by \"peer pressure\". For large-scale networks, efficient identification of multiple influential spreaders with a linear algorithm in threshold models that exhibit a first-order transition still remains a challenging task. Here we address this issue by exploring the collective influence in general threshold models of behavior cascading. Our analysis reveals that the importance of spreaders is fixed by the subcritical paths along which cascades propagate","authors_text":"Flaviano Morone, Hern\\'an A. Makse, Jeffrey Shaman, Sen Pei, Xian Teng","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-06-08T20:25:04Z","title":"Efficient collective influence maximization in cascading processes with first-order transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02739","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":"sha256:9718aeee7492a8d311425aac8d73a905823a8ac349b986a555569ac9089c7a1c","target":"record","created_at":"2026-05-18T00:48:42Z","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":"368c6586978236a718895a5a81859b4a4121aeb87f7779505271f8013dd46dfb","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-06-08T20:25:04Z","title_canon_sha256":"0cfdd9376845bf022d7a28c272b2570fdacf506128f67fb97fbeaf5062d7e52a"},"schema_version":"1.0","source":{"id":"1606.02739","kind":"arxiv","version":3}},"canonical_sha256":"d73f62c4ac33ff002f588fce9c84eaf7846d186c77d3e0ca3d53fd9f412df367","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d73f62c4ac33ff002f588fce9c84eaf7846d186c77d3e0ca3d53fd9f412df367","first_computed_at":"2026-05-18T00:48:42.683694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:42.683694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gc62t73kWudfPOSjj8L7PoJzFljWJI44L0UobNhcy2nGb4wep3kZjHRQOoepQ3z0LPliokljo9/4I185GyDZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:42.684123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02739","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9718aeee7492a8d311425aac8d73a905823a8ac349b986a555569ac9089c7a1c","sha256:d0f1d091bd94753175c4f2b11aee571dca1e1cac6c78bd817352a3ac5ebcb0b4"],"state_sha256":"4866a7246af90c497c45ee2eebf6dd1232278f275a1096da55922f7b2ca936e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RWFdieX+Z1PkeKASYJTEI3hlUQDi3ITqdj5aGr9UHfbiRE3lsHh1invSfVvrOgzbjaxCV55RE4x9SuiW9yTvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:13:18.723421Z","bundle_sha256":"1d333245a8dc9b668c8b35d72ce758baeff4288f78f473b3da17e5484f31bf5e"}}