{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KXI3GNL5AL7BBOR2MMEEP2ZM45","short_pith_number":"pith:KXI3GNL5","canonical_record":{"source":{"id":"1008.2314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-08-13T13:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"a250371a9a52a93439f9ab581bd6a6b106cff60cc242d2c436add54f2c26a24f","abstract_canon_sha256":"51030a2845a108892ba4780354b32bcfac047c0a6512c05fe48a7f29eea79b57"},"schema_version":"1.0"},"canonical_sha256":"55d1b3357d02fe10ba3a630847eb2ce74de0506ab80f48a881b660bc25adc387","source":{"kind":"arxiv","id":"1008.2314","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2314","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2314v1","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2314","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"KXI3GNL5AL7B","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KXI3GNL5AL7BBOR2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KXI3GNL5","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KXI3GNL5AL7BBOR2MMEEP2ZM45","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-08-13T13:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"a250371a9a52a93439f9ab581bd6a6b106cff60cc242d2c436add54f2c26a24f","abstract_canon_sha256":"51030a2845a108892ba4780354b32bcfac047c0a6512c05fe48a7f29eea79b57"},"schema_version":"1.0"},"canonical_sha256":"55d1b3357d02fe10ba3a630847eb2ce74de0506ab80f48a881b660bc25adc387","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:14.213948Z","signature_b64":"YBAuIQAm8BehWugN2kYr6RZEN3e5PzuYU8SRbZrKlLDF2ggRkfeNvOZETO/2S9LXJ+cvk0giv+fQDpUZdeP3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55d1b3357d02fe10ba3a630847eb2ce74de0506ab80f48a881b660bc25adc387","last_reissued_at":"2026-05-18T04:42:14.213467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:14.213467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2314","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":"2026-05-18T04:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFN/3AQbJ5PGf47svz++ThdFsx0p3A/gWmeGa7Y2tbT6RjC3Xk7iwe/NW1/IwszLz+/C5buqoLH6O6PdxEz0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:58:42.265063Z"},"content_sha256":"2abc56b6d46291de5e81e1ce1e54297e75d869608362355d0661e6b081784462","schema_version":"1.0","event_id":"sha256:2abc56b6d46291de5e81e1ce1e54297e75d869608362355d0661e6b081784462"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KXI3GNL5AL7BBOR2MMEEP2ZM45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on an NSFD Scheme for a Mathematical Model of Respiratory Virus Transmission","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Ronald E. Mickens, Talitha M. Washington","submitted_at":"2010-08-13T13:36:23Z","abstract_excerpt":"We construct a nonstandard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by R. E. Mickens. By use of an exact conservation law satisfied by the SIRS differential equations, we are able to determine the corresponding denominator function for the discrete first-order time derivatives. Our scheme is dynamically consistent with the SIRS differential equations since the conservation laws are preserved. Further, the scheme is shown to satisfy a positivity condition fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2314","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":"2026-05-18T04:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qfeQhYWY34VIJTUMi41l3qynZFGc3W5cAVOrgMTeRlHJRs/vjQLhSP2MHnj8XcUFWUQ72d9t7LXuYJWUGG//BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:58:42.265422Z"},"content_sha256":"7f9fd0eb5a87dc052a41e740970ee6a05233040b7ccdbf5d7ff860ec6d28e9e2","schema_version":"1.0","event_id":"sha256:7f9fd0eb5a87dc052a41e740970ee6a05233040b7ccdbf5d7ff860ec6d28e9e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/bundle.json","state_url":"https://pith.science/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/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":"2026-06-27T16:58:42Z","links":{"resolver":"https://pith.science/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45","bundle":"https://pith.science/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/bundle.json","state":"https://pith.science/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXI3GNL5AL7BBOR2MMEEP2ZM45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KXI3GNL5AL7BBOR2MMEEP2ZM45","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":"51030a2845a108892ba4780354b32bcfac047c0a6512c05fe48a7f29eea79b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-08-13T13:36:23Z","title_canon_sha256":"a250371a9a52a93439f9ab581bd6a6b106cff60cc242d2c436add54f2c26a24f"},"schema_version":"1.0","source":{"id":"1008.2314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2314","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2314v1","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2314","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"KXI3GNL5AL7B","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KXI3GNL5AL7BBOR2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KXI3GNL5","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7f9fd0eb5a87dc052a41e740970ee6a05233040b7ccdbf5d7ff860ec6d28e9e2","target":"graph","created_at":"2026-05-18T04:42:14Z","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 construct a nonstandard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by R. E. Mickens. By use of an exact conservation law satisfied by the SIRS differential equations, we are able to determine the corresponding denominator function for the discrete first-order time derivatives. Our scheme is dynamically consistent with the SIRS differential equations since the conservation laws are preserved. Further, the scheme is shown to satisfy a positivity condition fo","authors_text":"Ronald E. Mickens, Talitha M. Washington","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-08-13T13:36:23Z","title":"A Note on an NSFD Scheme for a Mathematical Model of Respiratory Virus Transmission"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2314","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":"sha256:2abc56b6d46291de5e81e1ce1e54297e75d869608362355d0661e6b081784462","target":"record","created_at":"2026-05-18T04:42:14Z","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":"51030a2845a108892ba4780354b32bcfac047c0a6512c05fe48a7f29eea79b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-08-13T13:36:23Z","title_canon_sha256":"a250371a9a52a93439f9ab581bd6a6b106cff60cc242d2c436add54f2c26a24f"},"schema_version":"1.0","source":{"id":"1008.2314","kind":"arxiv","version":1}},"canonical_sha256":"55d1b3357d02fe10ba3a630847eb2ce74de0506ab80f48a881b660bc25adc387","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55d1b3357d02fe10ba3a630847eb2ce74de0506ab80f48a881b660bc25adc387","first_computed_at":"2026-05-18T04:42:14.213467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:14.213467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBAuIQAm8BehWugN2kYr6RZEN3e5PzuYU8SRbZrKlLDF2ggRkfeNvOZETO/2S9LXJ+cvk0giv+fQDpUZdeP3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:14.213948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2abc56b6d46291de5e81e1ce1e54297e75d869608362355d0661e6b081784462","sha256:7f9fd0eb5a87dc052a41e740970ee6a05233040b7ccdbf5d7ff860ec6d28e9e2"],"state_sha256":"a455d9a4be6bf3a24f86df78fe2ce89dc45927fd78af495862afd598de1474a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4jQ9t7PLeYoGsZFYP5vFWXqPXgfnfzZ1TEdh16LFqQAw1A5PX1qr6bcomfPPfgnJ82nPD2sGcvXyPTCfwodDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:58:42.267296Z","bundle_sha256":"b64017140a9a4262a4a3aee6f491309977d213a88b7f983f16720d5668bb3079"}}