{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:23AROPGNSWMYOTHXOGE4JX3LWN","short_pith_number":"pith:23AROPGN","canonical_record":{"source":{"id":"1703.05644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-03-16T14:35:53Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"af863b35909b782df70a94ea2abd466868fe937d9da4ebe8fda307c09a801e63","abstract_canon_sha256":"7fadb266cb1c7d331d4412e6f5dfc0f5910bef1383903278e0dc844424d66601"},"schema_version":"1.0"},"canonical_sha256":"d6c1173ccd9599874cf77189c4df6bb37d963cd1dc39172aa0b82cec7542aa33","source":{"kind":"arxiv","id":"1703.05644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05644","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05644v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05644","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"23AROPGNSWMY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"23AROPGNSWMYOTHX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"23AROPGN","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:23AROPGNSWMYOTHXOGE4JX3LWN","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-03-16T14:35:53Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"af863b35909b782df70a94ea2abd466868fe937d9da4ebe8fda307c09a801e63","abstract_canon_sha256":"7fadb266cb1c7d331d4412e6f5dfc0f5910bef1383903278e0dc844424d66601"},"schema_version":"1.0"},"canonical_sha256":"d6c1173ccd9599874cf77189c4df6bb37d963cd1dc39172aa0b82cec7542aa33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.685201Z","signature_b64":"1cTLeVUimFxRb9qm0fZe1lkecriBCAkWjZSBul7OA5DR/ICc4ADpOx1PbIRRETpp4fWrq47kIrNqO2fHuQjWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6c1173ccd9599874cf77189c4df6bb37d963cd1dc39172aa0b82cec7542aa33","last_reissued_at":"2026-05-18T00:38:13.684514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.684514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05644","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cz1hdkU9ebU4gMgI2AW5dJ1I2kxIKTYV3Q8BjlkAAXcgvBTo8sAZnNiAPz5ky01AAfkOmnTa8g9Uv4e7k2uBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:52:30.539190Z"},"content_sha256":"72907a0b5a0065602570db4fdf428025afbffdd34071df7f39efafb396714ef8","schema_version":"1.0","event_id":"sha256:72907a0b5a0065602570db4fdf428025afbffdd34071df7f39efafb396714ef8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:23AROPGNSWMYOTHXOGE4JX3LWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ranking influential spreaders is an ill-defined problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Jain Gu, Jari Saram\\\"aki, Petter Holme, Sungmin Lee","submitted_at":"2017-03-16T14:35:53Z","abstract_excerpt":"Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem -- methods for identifying influential spreaders rank nodes according to how influential they are. In this work, we show that the ranking approach does not necessarily work: the set of most influential nodes depends on the number of nodes in the set. Therefore, the set of $n$ most important nodes to vaccinate does not need to have any node in common with the set of $n+1$ most import"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05644","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34i5iOeXx7nSiFnt4pUOn27PnFcfQrEJ1xcN4dsacQhqZ0mrhAjkbW70yj7GQbTYKY2wN9uRwS201x5WY5MIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:52:30.539567Z"},"content_sha256":"e042c7ef295946de16a7cd586a07fef8762c090c842cadfc3302c847c3558c1b","schema_version":"1.0","event_id":"sha256:e042c7ef295946de16a7cd586a07fef8762c090c842cadfc3302c847c3558c1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23AROPGNSWMYOTHXOGE4JX3LWN/bundle.json","state_url":"https://pith.science/pith/23AROPGNSWMYOTHXOGE4JX3LWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23AROPGNSWMYOTHXOGE4JX3LWN/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":"2026-05-28T22:52:30Z","links":{"resolver":"https://pith.science/pith/23AROPGNSWMYOTHXOGE4JX3LWN","bundle":"https://pith.science/pith/23AROPGNSWMYOTHXOGE4JX3LWN/bundle.json","state":"https://pith.science/pith/23AROPGNSWMYOTHXOGE4JX3LWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23AROPGNSWMYOTHXOGE4JX3LWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:23AROPGNSWMYOTHXOGE4JX3LWN","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":"7fadb266cb1c7d331d4412e6f5dfc0f5910bef1383903278e0dc844424d66601","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-03-16T14:35:53Z","title_canon_sha256":"af863b35909b782df70a94ea2abd466868fe937d9da4ebe8fda307c09a801e63"},"schema_version":"1.0","source":{"id":"1703.05644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05644","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05644v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05644","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"23AROPGNSWMY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"23AROPGNSWMYOTHX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"23AROPGN","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:e042c7ef295946de16a7cd586a07fef8762c090c842cadfc3302c847c3558c1b","target":"graph","created_at":"2026-05-18T00:38:13Z","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":"Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem -- methods for identifying influential spreaders rank nodes according to how influential they are. In this work, we show that the ranking approach does not necessarily work: the set of most influential nodes depends on the number of nodes in the set. Therefore, the set of $n$ most important nodes to vaccinate does not need to have any node in common with the set of $n+1$ most import","authors_text":"Jain Gu, Jari Saram\\\"aki, Petter Holme, Sungmin Lee","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-03-16T14:35:53Z","title":"Ranking influential spreaders is an ill-defined problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05644","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":"sha256:72907a0b5a0065602570db4fdf428025afbffdd34071df7f39efafb396714ef8","target":"record","created_at":"2026-05-18T00:38:13Z","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":"7fadb266cb1c7d331d4412e6f5dfc0f5910bef1383903278e0dc844424d66601","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-03-16T14:35:53Z","title_canon_sha256":"af863b35909b782df70a94ea2abd466868fe937d9da4ebe8fda307c09a801e63"},"schema_version":"1.0","source":{"id":"1703.05644","kind":"arxiv","version":1}},"canonical_sha256":"d6c1173ccd9599874cf77189c4df6bb37d963cd1dc39172aa0b82cec7542aa33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6c1173ccd9599874cf77189c4df6bb37d963cd1dc39172aa0b82cec7542aa33","first_computed_at":"2026-05-18T00:38:13.684514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.684514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1cTLeVUimFxRb9qm0fZe1lkecriBCAkWjZSBul7OA5DR/ICc4ADpOx1PbIRRETpp4fWrq47kIrNqO2fHuQjWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.685201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72907a0b5a0065602570db4fdf428025afbffdd34071df7f39efafb396714ef8","sha256:e042c7ef295946de16a7cd586a07fef8762c090c842cadfc3302c847c3558c1b"],"state_sha256":"b3eee4f08bb542ea1ebe429829cd98c0794fc7c6fee15f2e65051e2227113fb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Abq5C98iYzUlnNmBvnGNmRIUVOCKIxb9Rn04wcF7XsNdvoQaXqlMp46kL6blDWa4X1tjl2yn3bCsZw+chBdKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:52:30.541557Z","bundle_sha256":"e1bbee00813e0548e5f724a252c3bee1a580db592cc7d162e2a493c60f466b0f"}}