{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H26BDZYWP2WOMHVXBJ7TKE6TEM","short_pith_number":"pith:H26BDZYW","canonical_record":{"source":{"id":"1802.04037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T13:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"fcd651ed0b631a43ff27eefbe209d19db083be3a19b5a68c2fdcb97f5ac1dfb4","abstract_canon_sha256":"b3f199e00bfe67758f6f43da068e17c11aebc8da6660aae84767f4812f1a4882"},"schema_version":"1.0"},"canonical_sha256":"3ebc11e7167eace61eb70a7f3513d3233c781ebc9f96917a6623c1987ecd2c2d","source":{"kind":"arxiv","id":"1802.04037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04037","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04037v1","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04037","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"H26BDZYWP2WO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"H26BDZYWP2WOMHVX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"H26BDZYW","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H26BDZYWP2WOMHVXBJ7TKE6TEM","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T13:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"fcd651ed0b631a43ff27eefbe209d19db083be3a19b5a68c2fdcb97f5ac1dfb4","abstract_canon_sha256":"b3f199e00bfe67758f6f43da068e17c11aebc8da6660aae84767f4812f1a4882"},"schema_version":"1.0"},"canonical_sha256":"3ebc11e7167eace61eb70a7f3513d3233c781ebc9f96917a6623c1987ecd2c2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:49.638599Z","signature_b64":"ln1naEA3jal9XEksNgnVOLEPtVFQgGwyYeWEWjjGDbilssWpep90cX87oMlgru7gEDBVGD9bxUWb1cgIp9lZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ebc11e7167eace61eb70a7f3513d3233c781ebc9f96917a6623c1987ecd2c2d","last_reissued_at":"2026-05-18T00:23:49.637908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:49.637908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04037","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":"2026-05-18T00:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zN71iuGbPiS7fzIY0PW+/ov4XLI0m/wQ0H5ec4gI1Pi7IzaMCEYQaIE2b5brXezVPtu99QRwkf1DUa70hpJVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:43:04.032208Z"},"content_sha256":"aefe244be1241276233ab422e4cc163ff2228f238a74f01f0fc3ee3aff8b82d6","schema_version":"1.0","event_id":"sha256:aefe244be1241276233ab422e4cc163ff2228f238a74f01f0fc3ee3aff8b82d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H26BDZYWP2WOMHVXBJ7TKE6TEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extinction time for the weaker of two competing SIS epidemics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lopes, Malwina Luczak","submitted_at":"2018-02-12T13:40:03Z","abstract_excerpt":"We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic logistic SIS epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04037","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":"2026-05-18T00:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sHWlir+3SV4xctIPrLwd1ic/G0SMW1Xu4/v0Db+6Pa7mJMpakqfZhYEA18U+Od/PFdSpp3n/Isd1uQBuW0acDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:43:04.032568Z"},"content_sha256":"739a27eac5dbe0c7d4b8ef953ef9e947c9a2ec76fdbe7e1b8200d836b9d5de52","schema_version":"1.0","event_id":"sha256:739a27eac5dbe0c7d4b8ef953ef9e947c9a2ec76fdbe7e1b8200d836b9d5de52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/bundle.json","state_url":"https://pith.science/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/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":"2026-07-03T09:43:04Z","links":{"resolver":"https://pith.science/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM","bundle":"https://pith.science/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/bundle.json","state":"https://pith.science/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H26BDZYWP2WOMHVXBJ7TKE6TEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H26BDZYWP2WOMHVXBJ7TKE6TEM","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":"b3f199e00bfe67758f6f43da068e17c11aebc8da6660aae84767f4812f1a4882","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T13:40:03Z","title_canon_sha256":"fcd651ed0b631a43ff27eefbe209d19db083be3a19b5a68c2fdcb97f5ac1dfb4"},"schema_version":"1.0","source":{"id":"1802.04037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04037","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04037v1","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04037","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"H26BDZYWP2WO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"H26BDZYWP2WOMHVX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"H26BDZYW","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:739a27eac5dbe0c7d4b8ef953ef9e947c9a2ec76fdbe7e1b8200d836b9d5de52","target":"graph","created_at":"2026-05-18T00:23:49Z","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":"We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic logistic SIS epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (tha","authors_text":"Fabio Lopes, Malwina Luczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T13:40:03Z","title":"Extinction time for the weaker of two competing SIS epidemics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04037","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:aefe244be1241276233ab422e4cc163ff2228f238a74f01f0fc3ee3aff8b82d6","target":"record","created_at":"2026-05-18T00:23:49Z","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":"b3f199e00bfe67758f6f43da068e17c11aebc8da6660aae84767f4812f1a4882","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T13:40:03Z","title_canon_sha256":"fcd651ed0b631a43ff27eefbe209d19db083be3a19b5a68c2fdcb97f5ac1dfb4"},"schema_version":"1.0","source":{"id":"1802.04037","kind":"arxiv","version":1}},"canonical_sha256":"3ebc11e7167eace61eb70a7f3513d3233c781ebc9f96917a6623c1987ecd2c2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ebc11e7167eace61eb70a7f3513d3233c781ebc9f96917a6623c1987ecd2c2d","first_computed_at":"2026-05-18T00:23:49.637908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:49.637908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ln1naEA3jal9XEksNgnVOLEPtVFQgGwyYeWEWjjGDbilssWpep90cX87oMlgru7gEDBVGD9bxUWb1cgIp9lZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:49.638599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aefe244be1241276233ab422e4cc163ff2228f238a74f01f0fc3ee3aff8b82d6","sha256:739a27eac5dbe0c7d4b8ef953ef9e947c9a2ec76fdbe7e1b8200d836b9d5de52"],"state_sha256":"7a67528a26622ccb1cb8a2a3428688e7a65f5a8e3f5ccec877480fa930feab61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"teseYatge20l/KwsvJ5XfCSsu98MJA/0ESt8m16L1KcTshBRsM0VJ3pafCxUb0VWcar1f58QLRy380iyv+OGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T09:43:04.034499Z","bundle_sha256":"a914dbfacded8ba4cf3ba5c8a91ab0aedb6d9f803e7fd3d3a443e25c70a2b06a"}}