{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MI6MB5TFMM3JYOBKJMERNPYWUX","short_pith_number":"pith:MI6MB5TF","canonical_record":{"source":{"id":"1810.10799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-25T09:18:36Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"07c357ed439ab0012a69e715d582185930fea7bd6f9c623fca1189c948426b0c","abstract_canon_sha256":"4f1056db519cd63d757edcb42c312fe9b2a0ada345c814d9ca5684a4c4832cce"},"schema_version":"1.0"},"canonical_sha256":"623cc0f66563369c382a4b0916bf16a5e424a3512913cb48aba74ebf1a191005","source":{"kind":"arxiv","id":"1810.10799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10799","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10799v1","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10799","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"pith_short_12","alias_value":"MI6MB5TFMM3J","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MI6MB5TFMM3JYOBK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MI6MB5TF","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MI6MB5TFMM3JYOBKJMERNPYWUX","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-25T09:18:36Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"07c357ed439ab0012a69e715d582185930fea7bd6f9c623fca1189c948426b0c","abstract_canon_sha256":"4f1056db519cd63d757edcb42c312fe9b2a0ada345c814d9ca5684a4c4832cce"},"schema_version":"1.0"},"canonical_sha256":"623cc0f66563369c382a4b0916bf16a5e424a3512913cb48aba74ebf1a191005","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:04.400147Z","signature_b64":"g6uKWH7EnZdl84sI+eEmEr6hOtCOdEbFgRSnsluUmK2YjyoBfj/X34fYfJnz3w0wKXbkuIaT8gg/hsuGiSylDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"623cc0f66563369c382a4b0916bf16a5e424a3512913cb48aba74ebf1a191005","last_reissued_at":"2026-05-17T23:59:04.399761Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:04.399761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10799","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":"2026-05-17T23:59:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QuMHSn0vytRnuMdockDVQO62kXj85nAuPaZrZCvSPn+XcRwJQXoABuXxS+uEmI2Z1P6wkgMtEzlgj3rYnqzsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:40:15.701686Z"},"content_sha256":"b66280626b7d2410d49df6641c89e10797fafda1e0ba141f1b4f76a4bde5efce","schema_version":"1.0","event_id":"sha256:b66280626b7d2410d49df6641c89e10797fafda1e0ba141f1b4f76a4bde5efce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MI6MB5TFMM3JYOBKJMERNPYWUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relevance of backtracking paths in epidemic spreading on networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Claudio Castellano, Romualdo Pastor-Satorras","submitted_at":"2018-10-25T09:18:36Z","abstract_excerpt":"The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow to derive exact results for irreversible spreading (i.e. diseases with permanent acquired immunity) in locally-tree like topologies. This success has suggested the application of the same approach to reversible epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e. an individual is reinfected by a neighbor he/she previously infected) do not play a relevant role. In this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10799","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":"2026-05-17T23:59:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fbkrnfYtCrEyA+3NkCHHtfvpCYGrfWMMmua5t++on6PbzSqiH7XRGN5fCBMwI6xQSdat7qhchX04okej6PLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:40:15.702028Z"},"content_sha256":"8c5c8c016bd7cd57d9bd9752531e227d6b4fe78f00d9f5fa501297c16fc26609","schema_version":"1.0","event_id":"sha256:8c5c8c016bd7cd57d9bd9752531e227d6b4fe78f00d9f5fa501297c16fc26609"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/bundle.json","state_url":"https://pith.science/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/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":"2026-06-29T15:40:15Z","links":{"resolver":"https://pith.science/pith/MI6MB5TFMM3JYOBKJMERNPYWUX","bundle":"https://pith.science/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/bundle.json","state":"https://pith.science/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MI6MB5TFMM3JYOBKJMERNPYWUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MI6MB5TFMM3JYOBKJMERNPYWUX","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":"4f1056db519cd63d757edcb42c312fe9b2a0ada345c814d9ca5684a4c4832cce","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-25T09:18:36Z","title_canon_sha256":"07c357ed439ab0012a69e715d582185930fea7bd6f9c623fca1189c948426b0c"},"schema_version":"1.0","source":{"id":"1810.10799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10799","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10799v1","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10799","created_at":"2026-05-17T23:59:04Z"},{"alias_kind":"pith_short_12","alias_value":"MI6MB5TFMM3J","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MI6MB5TFMM3JYOBK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MI6MB5TF","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:8c5c8c016bd7cd57d9bd9752531e227d6b4fe78f00d9f5fa501297c16fc26609","target":"graph","created_at":"2026-05-17T23:59:04Z","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":"The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow to derive exact results for irreversible spreading (i.e. diseases with permanent acquired immunity) in locally-tree like topologies. This success has suggested the application of the same approach to reversible epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e. an individual is reinfected by a neighbor he/she previously infected) do not play a relevant role. In this pa","authors_text":"Claudio Castellano, Romualdo Pastor-Satorras","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-25T09:18:36Z","title":"Relevance of backtracking paths in epidemic spreading on networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10799","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:b66280626b7d2410d49df6641c89e10797fafda1e0ba141f1b4f76a4bde5efce","target":"record","created_at":"2026-05-17T23:59:04Z","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":"4f1056db519cd63d757edcb42c312fe9b2a0ada345c814d9ca5684a4c4832cce","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-10-25T09:18:36Z","title_canon_sha256":"07c357ed439ab0012a69e715d582185930fea7bd6f9c623fca1189c948426b0c"},"schema_version":"1.0","source":{"id":"1810.10799","kind":"arxiv","version":1}},"canonical_sha256":"623cc0f66563369c382a4b0916bf16a5e424a3512913cb48aba74ebf1a191005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"623cc0f66563369c382a4b0916bf16a5e424a3512913cb48aba74ebf1a191005","first_computed_at":"2026-05-17T23:59:04.399761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:04.399761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g6uKWH7EnZdl84sI+eEmEr6hOtCOdEbFgRSnsluUmK2YjyoBfj/X34fYfJnz3w0wKXbkuIaT8gg/hsuGiSylDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:04.400147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b66280626b7d2410d49df6641c89e10797fafda1e0ba141f1b4f76a4bde5efce","sha256:8c5c8c016bd7cd57d9bd9752531e227d6b4fe78f00d9f5fa501297c16fc26609"],"state_sha256":"6e345f636dc089afd7025a990eaa6b474b11636f024b8de9f2dfb9a4bbf23de1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vo6Tjc76PS3JjfmXtkCStfKTRKOXi0PoW9t7g/ex4OsryZr2ojsnVPo/s9xywLE5sk7tjDqIfKzv0bewO54MDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:40:15.703876Z","bundle_sha256":"acaa9c1969e73140c7e23412ce32b3c5be9277abb23ac0ea5fb26b5c0b6358da"}}