{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JYZUFTJ4FNZ7LO5MJXU5R3FB3O","short_pith_number":"pith:JYZUFTJ4","canonical_record":{"source":{"id":"0906.5550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:49:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3c7d1f81a5a412c253da6f195ead1a70ba999a675855c6ed7ba4623345cbaeb3","abstract_canon_sha256":"607d52b544062f2de36150f7ea3454e05ad5e0145fbb3b400e66eb88f47198af"},"schema_version":"1.0"},"canonical_sha256":"4e3342cd3c2b73f5bbac4de9d8eca1dbae7ffeaa2ca1b36fb6c92b4a8c176202","source":{"kind":"arxiv","id":"0906.5550","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5550","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5550v2","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5550","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"JYZUFTJ4FNZ7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JYZUFTJ4FNZ7LO5M","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JYZUFTJ4","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JYZUFTJ4FNZ7LO5MJXU5R3FB3O","target":"record","payload":{"canonical_record":{"source":{"id":"0906.5550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:49:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3c7d1f81a5a412c253da6f195ead1a70ba999a675855c6ed7ba4623345cbaeb3","abstract_canon_sha256":"607d52b544062f2de36150f7ea3454e05ad5e0145fbb3b400e66eb88f47198af"},"schema_version":"1.0"},"canonical_sha256":"4e3342cd3c2b73f5bbac4de9d8eca1dbae7ffeaa2ca1b36fb6c92b4a8c176202","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:11.704449Z","signature_b64":"761J+LAvhM1QU1u7CvDn/XIpeSDCyY+EXurCqLsJ97o1Q6c82zxmTgd0C6evrHK1UR7dgLMjykZ2kwxxtUPUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e3342cd3c2b73f5bbac4de9d8eca1dbae7ffeaa2ca1b36fb6c92b4a8c176202","last_reissued_at":"2026-05-18T02:13:11.703877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:11.703877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.5550","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdwdwm9fqMvXjghhk8szllMrd3NbNL2ZG2LNDIn8hrttR2hrqe+Etc54M0xM5hbC1KaSFVgVDcN/cR+C84gNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:17:20.651632Z"},"content_sha256":"0706ea60e1d629cfee4ef72d4d7ad4a19c9858223552157ac5bf016936095848","schema_version":"1.0","event_id":"sha256:0706ea60e1d629cfee4ef72d4d7ad4a19c9858223552157ac5bf016936095848"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JYZUFTJ4FNZ7LO5MJXU5R3FB3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"WKB theory of epidemic fade-out in stochastic populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.PE","authors_text":"Baruch Meerson, Pavel V. Sasorov","submitted_at":"2009-06-30T14:49:00Z","abstract_excerpt":"Stochastic effects may cause fade-out of an infectious disease in a population immediately after an epidemic outbreak. We develop WKB theory to determine the most probable path of the system toward epidemic fade-out and to evaluate the fade-out probability. The most probable path is an instanton-like orbit in the phase space of the underlying Hamiltonian flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5550","kind":"arxiv","version":2},"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":"2026-05-18T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4vgVOTcwbyzjzN/OBLNVCpucTZcPoRq3vXwGyR6yP0NMKJ7n8ZVkSWsPLtqi3up63x2H3WLOHIf1zuxXjKPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:17:20.652358Z"},"content_sha256":"e4c93d01d5f05b4e824ff9a777277b2e444da726ed4237975ce48a40af16f02c","schema_version":"1.0","event_id":"sha256:e4c93d01d5f05b4e824ff9a777277b2e444da726ed4237975ce48a40af16f02c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/bundle.json","state_url":"https://pith.science/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/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":"2026-06-08T03:17:20Z","links":{"resolver":"https://pith.science/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O","bundle":"https://pith.science/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/bundle.json","state":"https://pith.science/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYZUFTJ4FNZ7LO5MJXU5R3FB3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JYZUFTJ4FNZ7LO5MJXU5R3FB3O","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":"607d52b544062f2de36150f7ea3454e05ad5e0145fbb3b400e66eb88f47198af","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:49:00Z","title_canon_sha256":"3c7d1f81a5a412c253da6f195ead1a70ba999a675855c6ed7ba4623345cbaeb3"},"schema_version":"1.0","source":{"id":"0906.5550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5550","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5550v2","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5550","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"JYZUFTJ4FNZ7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JYZUFTJ4FNZ7LO5M","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JYZUFTJ4","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:e4c93d01d5f05b4e824ff9a777277b2e444da726ed4237975ce48a40af16f02c","target":"graph","created_at":"2026-05-18T02:13:11Z","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":"Stochastic effects may cause fade-out of an infectious disease in a population immediately after an epidemic outbreak. We develop WKB theory to determine the most probable path of the system toward epidemic fade-out and to evaluate the fade-out probability. The most probable path is an instanton-like orbit in the phase space of the underlying Hamiltonian flow.","authors_text":"Baruch Meerson, Pavel V. Sasorov","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:49:00Z","title":"WKB theory of epidemic fade-out in stochastic populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5550","kind":"arxiv","version":2},"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":"sha256:0706ea60e1d629cfee4ef72d4d7ad4a19c9858223552157ac5bf016936095848","target":"record","created_at":"2026-05-18T02:13:11Z","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":"607d52b544062f2de36150f7ea3454e05ad5e0145fbb3b400e66eb88f47198af","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:49:00Z","title_canon_sha256":"3c7d1f81a5a412c253da6f195ead1a70ba999a675855c6ed7ba4623345cbaeb3"},"schema_version":"1.0","source":{"id":"0906.5550","kind":"arxiv","version":2}},"canonical_sha256":"4e3342cd3c2b73f5bbac4de9d8eca1dbae7ffeaa2ca1b36fb6c92b4a8c176202","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e3342cd3c2b73f5bbac4de9d8eca1dbae7ffeaa2ca1b36fb6c92b4a8c176202","first_computed_at":"2026-05-18T02:13:11.703877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:11.703877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"761J+LAvhM1QU1u7CvDn/XIpeSDCyY+EXurCqLsJ97o1Q6c82zxmTgd0C6evrHK1UR7dgLMjykZ2kwxxtUPUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:11.704449Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0706ea60e1d629cfee4ef72d4d7ad4a19c9858223552157ac5bf016936095848","sha256:e4c93d01d5f05b4e824ff9a777277b2e444da726ed4237975ce48a40af16f02c"],"state_sha256":"b582c5fc638393da476c14894496c95ab3a40b86ff31516f46b2d0e1d22bae51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkbvGQWrfpjRICGB1kXouFMNAcazfxJMoNNOQmAeimXK0oU3Be8CfoopYf4dvKn4FRzSatZcqbReMZWP/CYsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:17:20.656347Z","bundle_sha256":"d4bf10560409891b1628cf14d5eaa48857d16b857bd73014b559c7ff2989d052"}}