{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SZFMZ7ZRZHPSTD5IBMBTN4TQAT","short_pith_number":"pith:SZFMZ7ZR","canonical_record":{"source":{"id":"1406.0877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-03T21:02:47Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"58a4bef202045829052ca23618cafc46ce7f57ad3dd3d5bd607617c8aa819062","abstract_canon_sha256":"d5a7b03adcf040d4aa1ab715d0b11407a4c10e0fc014ef5dfe85785f90a1a22c"},"schema_version":"1.0"},"canonical_sha256":"964accff31c9df298fa80b0336f27004c5eac76192c5e4eae35c498d68bfb11e","source":{"kind":"arxiv","id":"1406.0877","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0877","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0877v1","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0877","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"SZFMZ7ZRZHPS","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZFMZ7ZRZHPSTD5I","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZFMZ7ZR","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SZFMZ7ZRZHPSTD5IBMBTN4TQAT","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-03T21:02:47Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"58a4bef202045829052ca23618cafc46ce7f57ad3dd3d5bd607617c8aa819062","abstract_canon_sha256":"d5a7b03adcf040d4aa1ab715d0b11407a4c10e0fc014ef5dfe85785f90a1a22c"},"schema_version":"1.0"},"canonical_sha256":"964accff31c9df298fa80b0336f27004c5eac76192c5e4eae35c498d68bfb11e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:43.726970Z","signature_b64":"IYJ5g+fA3mHpFgR2+VWlKTJ/a5HAv3ur8DvxG9Km/9FdM2NTR0nCxeJ0nEXpbS2DoRxliJcsa2ndvKIeBrR2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"964accff31c9df298fa80b0336f27004c5eac76192c5e4eae35c498d68bfb11e","last_reissued_at":"2026-05-18T02:47:43.726240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:43.726240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0877","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":"2026-05-18T02:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmkYo+fIY+DbtPp+8Tbw2NiXBMAy1dKSFUP/8pLMGB7LoLqL+ZmGOs+40FIDwJtsgXlswk156qjw6oXRdxvsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:08:49.424749Z"},"content_sha256":"f8425035aceb8c80bd444a89b72d03690c7375b4758722cd3a9868c12c71eea0","schema_version":"1.0","event_id":"sha256:f8425035aceb8c80bd444a89b72d03690c7375b4758722cd3a9868c12c71eea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SZFMZ7ZRZHPSTD5IBMBTN4TQAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling TB-HIV syndemic and treatment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.DS","authors_text":"Cristiana J. Silva, Delfim F. M. Torres","submitted_at":"2014-06-03T21:02:47Z","abstract_excerpt":"Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency syndrome (AIDS) treatment for individuals with only one of the infectious diseases or both. The basic reproduction number and equilibrium points are determined and stability is analyzed. Through simulations, we show that TB treatment for individuals with only TB infection reduces the number of individuals that become co-infected with TB and HIV/AIDS, and reduces "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0877","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":"2026-05-18T02:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2cCWLWkLM0jOCAtYKfTPYbLngtQaethVEC1HxV6YQVLJ1tlWarKGZOcD+xj6GfSmjRVWQYlkdV2bVhltwL5LBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:08:49.425089Z"},"content_sha256":"93d8c83b2240c81c7afc9d372672391cbc1f696d293cc3074dc6c1e418022551","schema_version":"1.0","event_id":"sha256:93d8c83b2240c81c7afc9d372672391cbc1f696d293cc3074dc6c1e418022551"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/bundle.json","state_url":"https://pith.science/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/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":"2026-06-27T05:08:49Z","links":{"resolver":"https://pith.science/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT","bundle":"https://pith.science/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/bundle.json","state":"https://pith.science/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZFMZ7ZRZHPSTD5IBMBTN4TQAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SZFMZ7ZRZHPSTD5IBMBTN4TQAT","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":"d5a7b03adcf040d4aa1ab715d0b11407a4c10e0fc014ef5dfe85785f90a1a22c","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-03T21:02:47Z","title_canon_sha256":"58a4bef202045829052ca23618cafc46ce7f57ad3dd3d5bd607617c8aa819062"},"schema_version":"1.0","source":{"id":"1406.0877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0877","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0877v1","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0877","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"SZFMZ7ZRZHPS","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZFMZ7ZRZHPSTD5I","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZFMZ7ZR","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:93d8c83b2240c81c7afc9d372672391cbc1f696d293cc3074dc6c1e418022551","target":"graph","created_at":"2026-05-18T02:47:43Z","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":"Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency syndrome (AIDS) treatment for individuals with only one of the infectious diseases or both. The basic reproduction number and equilibrium points are determined and stability is analyzed. Through simulations, we show that TB treatment for individuals with only TB infection reduces the number of individuals that become co-infected with TB and HIV/AIDS, and reduces ","authors_text":"Cristiana J. Silva, Delfim F. M. Torres","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-03T21:02:47Z","title":"Modeling TB-HIV syndemic and treatment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0877","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:f8425035aceb8c80bd444a89b72d03690c7375b4758722cd3a9868c12c71eea0","target":"record","created_at":"2026-05-18T02:47:43Z","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":"d5a7b03adcf040d4aa1ab715d0b11407a4c10e0fc014ef5dfe85785f90a1a22c","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-03T21:02:47Z","title_canon_sha256":"58a4bef202045829052ca23618cafc46ce7f57ad3dd3d5bd607617c8aa819062"},"schema_version":"1.0","source":{"id":"1406.0877","kind":"arxiv","version":1}},"canonical_sha256":"964accff31c9df298fa80b0336f27004c5eac76192c5e4eae35c498d68bfb11e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"964accff31c9df298fa80b0336f27004c5eac76192c5e4eae35c498d68bfb11e","first_computed_at":"2026-05-18T02:47:43.726240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:43.726240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IYJ5g+fA3mHpFgR2+VWlKTJ/a5HAv3ur8DvxG9Km/9FdM2NTR0nCxeJ0nEXpbS2DoRxliJcsa2ndvKIeBrR2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:43.726970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8425035aceb8c80bd444a89b72d03690c7375b4758722cd3a9868c12c71eea0","sha256:93d8c83b2240c81c7afc9d372672391cbc1f696d293cc3074dc6c1e418022551"],"state_sha256":"8b4cfa8f8f06788a731a870a2a659e2a914dfe045c8027a4a0aa25d46a70861f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nw7stxm4qLQ8Cvgw1F3Ic4ruTOSoeA0I4cRGZ79CRWupOqV2Qz0RfKedq84kqeJ3I96V3Px7VZ8bvgWexiDNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:08:49.426966Z","bundle_sha256":"5fb3c3800fc2224dde4265ccde990a381d6c1930f06e734d635c442888a127e9"}}