{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:64KI2UGAXU4XNKHQN4K3AN43X7","short_pith_number":"pith:64KI2UGA","canonical_record":{"source":{"id":"1102.0987","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-04T18:19:01Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"f1b64f493dd16e9d3dc1924beb57fb96d3c2ffa4c93e80328d51c744072b1e62","abstract_canon_sha256":"1d6efb8d2256428ad200e570091c679c97a85ba7aaeae0ee540425b35f4870aa"},"schema_version":"1.0"},"canonical_sha256":"f7148d50c0bd3976a8f06f15b0379bbfc0faf1afe7b3cb7b8dfde0b952e8f768","source":{"kind":"arxiv","id":"1102.0987","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0987","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0987v3","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0987","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"64KI2UGAXU4X","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64KI2UGAXU4XNKHQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64KI2UGA","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:64KI2UGAXU4XNKHQN4K3AN43X7","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0987","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-04T18:19:01Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"f1b64f493dd16e9d3dc1924beb57fb96d3c2ffa4c93e80328d51c744072b1e62","abstract_canon_sha256":"1d6efb8d2256428ad200e570091c679c97a85ba7aaeae0ee540425b35f4870aa"},"schema_version":"1.0"},"canonical_sha256":"f7148d50c0bd3976a8f06f15b0379bbfc0faf1afe7b3cb7b8dfde0b952e8f768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:40.495866Z","signature_b64":"JW3T4qOexM4Tj0QD00aYedmkiuTbScEyJnxSPx7nTACbSvLsKx8+Dx8mFo+3xlqggpYZsyL7lxxJf7S3cHUKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7148d50c0bd3976a8f06f15b0379bbfc0faf1afe7b3cb7b8dfde0b952e8f768","last_reissued_at":"2026-05-18T02:22:40.495151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:40.495151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0987","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":"2026-05-18T02:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MOs8aHBroCae8rYo6S3FKkE6KQX8t6AqfL1Jysr0LZ9lXXBrdvD2uAgZgw73fRFou6BvSybUG1vouJ0duMQUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:01:44.792099Z"},"content_sha256":"b294cbc4433b9a3d947b28bee5b9360ff4eb31aaae56c073998952be5876f00b","schema_version":"1.0","event_id":"sha256:b294cbc4433b9a3d947b28bee5b9360ff4eb31aaae56c073998952be5876f00b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:64KI2UGAXU4XNKHQN4K3AN43X7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation on networks: an exact alternative perspective","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":"Antoine Allard, Laurent H\\'ebert-Dufresne, Louis J. Dub\\'e, Pierre-Andr\\'e No\\\"el, Vincent Marceau","submitted_at":"2011-02-04T18:19:01Z","abstract_excerpt":"By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-death Markov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximations and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0987","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":"2026-05-18T02:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dY3ROrPHXVreEFJAj677QvDzphPe6cqTS1UscWcoqXnD+ZcwWBska5BeLouVRappiG8DgDfrsai2qvSfO7/tDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:01:44.792474Z"},"content_sha256":"7873ee6715f20234341d28a152f843e288a4e9c3fc54d55cb6286831067f0e48","schema_version":"1.0","event_id":"sha256:7873ee6715f20234341d28a152f843e288a4e9c3fc54d55cb6286831067f0e48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64KI2UGAXU4XNKHQN4K3AN43X7/bundle.json","state_url":"https://pith.science/pith/64KI2UGAXU4XNKHQN4K3AN43X7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64KI2UGAXU4XNKHQN4K3AN43X7/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":"2026-05-22T18:01:44Z","links":{"resolver":"https://pith.science/pith/64KI2UGAXU4XNKHQN4K3AN43X7","bundle":"https://pith.science/pith/64KI2UGAXU4XNKHQN4K3AN43X7/bundle.json","state":"https://pith.science/pith/64KI2UGAXU4XNKHQN4K3AN43X7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64KI2UGAXU4XNKHQN4K3AN43X7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:64KI2UGAXU4XNKHQN4K3AN43X7","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":"1d6efb8d2256428ad200e570091c679c97a85ba7aaeae0ee540425b35f4870aa","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":"2011-02-04T18:19:01Z","title_canon_sha256":"f1b64f493dd16e9d3dc1924beb57fb96d3c2ffa4c93e80328d51c744072b1e62"},"schema_version":"1.0","source":{"id":"1102.0987","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0987","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0987v3","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0987","created_at":"2026-05-18T02:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"64KI2UGAXU4X","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64KI2UGAXU4XNKHQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64KI2UGA","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:7873ee6715f20234341d28a152f843e288a4e9c3fc54d55cb6286831067f0e48","target":"graph","created_at":"2026-05-18T02:22:40Z","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":"By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-death Markov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximations and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers","authors_text":"Antoine Allard, Laurent H\\'ebert-Dufresne, Louis J. Dub\\'e, Pierre-Andr\\'e No\\\"el, Vincent Marceau","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":"2011-02-04T18:19:01Z","title":"Propagation on networks: an exact alternative perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0987","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:b294cbc4433b9a3d947b28bee5b9360ff4eb31aaae56c073998952be5876f00b","target":"record","created_at":"2026-05-18T02:22:40Z","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":"1d6efb8d2256428ad200e570091c679c97a85ba7aaeae0ee540425b35f4870aa","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":"2011-02-04T18:19:01Z","title_canon_sha256":"f1b64f493dd16e9d3dc1924beb57fb96d3c2ffa4c93e80328d51c744072b1e62"},"schema_version":"1.0","source":{"id":"1102.0987","kind":"arxiv","version":3}},"canonical_sha256":"f7148d50c0bd3976a8f06f15b0379bbfc0faf1afe7b3cb7b8dfde0b952e8f768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7148d50c0bd3976a8f06f15b0379bbfc0faf1afe7b3cb7b8dfde0b952e8f768","first_computed_at":"2026-05-18T02:22:40.495151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:40.495151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JW3T4qOexM4Tj0QD00aYedmkiuTbScEyJnxSPx7nTACbSvLsKx8+Dx8mFo+3xlqggpYZsyL7lxxJf7S3cHUKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:40.495866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0987","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b294cbc4433b9a3d947b28bee5b9360ff4eb31aaae56c073998952be5876f00b","sha256:7873ee6715f20234341d28a152f843e288a4e9c3fc54d55cb6286831067f0e48"],"state_sha256":"be896a08413c9576b7458a503ce1daecba6eb93a8fa4bd5f2e4723c422c8c3fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghXjczwZ1XPD3Sw5/KgXuOXyVqn7L9uyIMzo8WR8sK+4rKU8eGBOEBEyNO5AwtGNMl36J0HTwR1K3n7R6fRuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:01:44.794538Z","bundle_sha256":"1c28193a6bd0e8295662dbf46fae4d8c347ae6886dfe2eb2b86c9c8729c740eb"}}