{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O4GUCQ5CFDU4OEXLHBJGTBUJC3","short_pith_number":"pith:O4GUCQ5C","canonical_record":{"source":{"id":"1812.09759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-23T19:16:11Z","cross_cats_sorted":["math.DS","physics.soc-ph"],"title_canon_sha256":"4e16bc621bf50774fae45d53c6ea76729b781d8b5c32a79dcdf8db9f342eddb1","abstract_canon_sha256":"8ecc162071abe1a4ef1d4c70cd7a020e0cb4985dae84ba963b4cd5d49a3d97e6"},"schema_version":"1.0"},"canonical_sha256":"770d4143a228e9c712eb385269868916dd6d578208f5b73f09eba2df93c8665d","source":{"kind":"arxiv","id":"1812.09759","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09759","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09759v1","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09759","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"O4GUCQ5CFDU4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O4GUCQ5CFDU4OEXL","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O4GUCQ5C","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O4GUCQ5CFDU4OEXLHBJGTBUJC3","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-23T19:16:11Z","cross_cats_sorted":["math.DS","physics.soc-ph"],"title_canon_sha256":"4e16bc621bf50774fae45d53c6ea76729b781d8b5c32a79dcdf8db9f342eddb1","abstract_canon_sha256":"8ecc162071abe1a4ef1d4c70cd7a020e0cb4985dae84ba963b4cd5d49a3d97e6"},"schema_version":"1.0"},"canonical_sha256":"770d4143a228e9c712eb385269868916dd6d578208f5b73f09eba2df93c8665d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:14.536064Z","signature_b64":"o5NguZFbyf3Uq+5Y9O9iOEFmiU3LRid8Q4sXHntoZVL/OF1BZndvmc4h6UV0LD3fDUW2cnA833IAwQpot0RyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"770d4143a228e9c712eb385269868916dd6d578208f5b73f09eba2df93c8665d","last_reissued_at":"2026-05-17T23:57:14.535479Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:14.535479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09759","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":"2026-05-17T23:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M92Wx7DBa9+iLLdjtC15TN7rOOCzWLcwfj/SbqwWVjeCJN2gmjath0hJucf2yfPI6LxWos0XxF8lpD2ug2XQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:06:49.425777Z"},"content_sha256":"11d552b6fcb904fdfcde207d9948793a9600367bea757906f08e6ec81142f156","schema_version":"1.0","event_id":"sha256:11d552b6fcb904fdfcde207d9948793a9600367bea757906f08e6ec81142f156"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O4GUCQ5CFDU4OEXLHBJGTBUJC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Solution to a Dynamic SIR Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","physics.soc-ph"],"primary_cat":"math.CA","authors_text":"Delfim F. M. Torres, Martin Bohner, Sabrina Streipert","submitted_at":"2018-12-23T19:16:11Z","abstract_excerpt":"We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible-infected-removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09759","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":"2026-05-17T23:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xcrZJJLIe+lhYEfi45O0/OUILJnRIr15907sPzMfdo0A21P1pXIMlKA1WF4C1kVqbNmW5BgpU+bHwrNISRwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:06:49.426116Z"},"content_sha256":"c986591c9a0a78ed05fc3b8c52f07276bb111bfd00530c7575fd667827e43d31","schema_version":"1.0","event_id":"sha256:c986591c9a0a78ed05fc3b8c52f07276bb111bfd00530c7575fd667827e43d31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/bundle.json","state_url":"https://pith.science/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/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":"2026-06-20T22:06:49Z","links":{"resolver":"https://pith.science/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3","bundle":"https://pith.science/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/bundle.json","state":"https://pith.science/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4GUCQ5CFDU4OEXLHBJGTBUJC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O4GUCQ5CFDU4OEXLHBJGTBUJC3","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":"8ecc162071abe1a4ef1d4c70cd7a020e0cb4985dae84ba963b4cd5d49a3d97e6","cross_cats_sorted":["math.DS","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-23T19:16:11Z","title_canon_sha256":"4e16bc621bf50774fae45d53c6ea76729b781d8b5c32a79dcdf8db9f342eddb1"},"schema_version":"1.0","source":{"id":"1812.09759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09759","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09759v1","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09759","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"O4GUCQ5CFDU4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O4GUCQ5CFDU4OEXL","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O4GUCQ5C","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:c986591c9a0a78ed05fc3b8c52f07276bb111bfd00530c7575fd667827e43d31","target":"graph","created_at":"2026-05-17T23:57:14Z","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 investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible-infected-removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the c","authors_text":"Delfim F. M. Torres, Martin Bohner, Sabrina Streipert","cross_cats":["math.DS","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-23T19:16:11Z","title":"Exact Solution to a Dynamic SIR Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09759","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":"sha256:11d552b6fcb904fdfcde207d9948793a9600367bea757906f08e6ec81142f156","target":"record","created_at":"2026-05-17T23:57:14Z","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":"8ecc162071abe1a4ef1d4c70cd7a020e0cb4985dae84ba963b4cd5d49a3d97e6","cross_cats_sorted":["math.DS","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-23T19:16:11Z","title_canon_sha256":"4e16bc621bf50774fae45d53c6ea76729b781d8b5c32a79dcdf8db9f342eddb1"},"schema_version":"1.0","source":{"id":"1812.09759","kind":"arxiv","version":1}},"canonical_sha256":"770d4143a228e9c712eb385269868916dd6d578208f5b73f09eba2df93c8665d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"770d4143a228e9c712eb385269868916dd6d578208f5b73f09eba2df93c8665d","first_computed_at":"2026-05-17T23:57:14.535479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:14.535479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5NguZFbyf3Uq+5Y9O9iOEFmiU3LRid8Q4sXHntoZVL/OF1BZndvmc4h6UV0LD3fDUW2cnA833IAwQpot0RyAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:14.536064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d552b6fcb904fdfcde207d9948793a9600367bea757906f08e6ec81142f156","sha256:c986591c9a0a78ed05fc3b8c52f07276bb111bfd00530c7575fd667827e43d31"],"state_sha256":"ace785aa52321b1d2c78779deaff33eb7ab6070a6faa457758b16bea218c736f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BB7roSd6qv0sR2hnnh6xilmNIN+buWXCTBbHT4QoXfrQXtaxpd5wFukaXs+aJItrzVMkabqsgVgAFUKispl8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:06:49.427974Z","bundle_sha256":"1ba023fdac206dcb0df0a88c7923551a9c67350213d262b4729e32767fb659cf"}}