{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TUHDHJDHAFP32HV5WCN4NRKRHN","short_pith_number":"pith:TUHDHJDH","canonical_record":{"source":{"id":"1601.05125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-19T22:40:34Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"4a001bf55040aa6b2c529f5d958a09ed94ac8da3245e6da781ecf3a284762d7a","abstract_canon_sha256":"b5755072a4834fbbe5fd977ddd24a1333001614ef87d480bcc700e662abcf5cf"},"schema_version":"1.0"},"canonical_sha256":"9d0e33a467015fbd1ebdb09bc6c5513b740c5f3739118ba6240d027380b34f30","source":{"kind":"arxiv","id":"1601.05125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05125","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05125v1","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05125","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"TUHDHJDHAFP3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TUHDHJDHAFP32HV5","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TUHDHJDH","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TUHDHJDHAFP32HV5WCN4NRKRHN","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-19T22:40:34Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"4a001bf55040aa6b2c529f5d958a09ed94ac8da3245e6da781ecf3a284762d7a","abstract_canon_sha256":"b5755072a4834fbbe5fd977ddd24a1333001614ef87d480bcc700e662abcf5cf"},"schema_version":"1.0"},"canonical_sha256":"9d0e33a467015fbd1ebdb09bc6c5513b740c5f3739118ba6240d027380b34f30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:16.069200Z","signature_b64":"GLpShEslRE1Th9u3It++c5qZ8lD49CkXZGCHugM6cvXl/z0vOa7GJ5MBDLixVi5CM7egTrkzjxcPYTOi4ULLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d0e33a467015fbd1ebdb09bc6c5513b740c5f3739118ba6240d027380b34f30","last_reissued_at":"2026-05-18T01:22:16.068570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:16.068570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05125","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":"2026-05-18T01:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UH/DstltV00MbV6Kx9JTMeU2Tr0sEBycSdnQZPbjkfNTRW/OSCT+8LQHxDr/VWN3WSk3SZmrdITOigV4v0XcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:59:31.759215Z"},"content_sha256":"3b6bd16eb8a2a0f37a66dd8e962a95e745a4c10af33b08fd2d6576e7b5201146","schema_version":"1.0","event_id":"sha256:3b6bd16eb8a2a0f37a66dd8e962a95e745a4c10af33b08fd2d6576e7b5201146"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TUHDHJDHAFP32HV5WCN4NRKRHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of periodic orbits for periodic eco-epidemic models with disease in the prey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.DS","authors_text":"C\\'esar M. Silva","submitted_at":"2016-01-19T22:40:34Z","abstract_excerpt":"For an eco-epidemic model with disease in the prey and periodic coefficients it is conjectured in [Xingge Niu, Tailei Zhang, Zhidong Teng, The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey, Applied Mathematical Modelling 35, 457-470 (2011)] that, when the infected prey is permanent, there is a positive periodic orbit that is globally asymptotically stable in the interior of $(\\R^+)^3$. In this paper we prove the existence part of the conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05125","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":"2026-05-18T01:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZE1YHWG95yG1EH3mqHvL90rE2OChTJ4GeHhmOQgPFwvRBO1NEEcnAcZXPHLLLucz/93o4/xU2TKti0aGotM8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:59:31.759569Z"},"content_sha256":"41816ae73828e85f95141cadf7dd14e13baa8143690ed8084615ee4f8cdf35ca","schema_version":"1.0","event_id":"sha256:41816ae73828e85f95141cadf7dd14e13baa8143690ed8084615ee4f8cdf35ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/bundle.json","state_url":"https://pith.science/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/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":"2026-06-04T02:59:31Z","links":{"resolver":"https://pith.science/pith/TUHDHJDHAFP32HV5WCN4NRKRHN","bundle":"https://pith.science/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/bundle.json","state":"https://pith.science/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUHDHJDHAFP32HV5WCN4NRKRHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TUHDHJDHAFP32HV5WCN4NRKRHN","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":"b5755072a4834fbbe5fd977ddd24a1333001614ef87d480bcc700e662abcf5cf","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-19T22:40:34Z","title_canon_sha256":"4a001bf55040aa6b2c529f5d958a09ed94ac8da3245e6da781ecf3a284762d7a"},"schema_version":"1.0","source":{"id":"1601.05125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05125","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05125v1","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05125","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"TUHDHJDHAFP3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TUHDHJDHAFP32HV5","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TUHDHJDH","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:41816ae73828e85f95141cadf7dd14e13baa8143690ed8084615ee4f8cdf35ca","target":"graph","created_at":"2026-05-18T01:22:16Z","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":"For an eco-epidemic model with disease in the prey and periodic coefficients it is conjectured in [Xingge Niu, Tailei Zhang, Zhidong Teng, The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey, Applied Mathematical Modelling 35, 457-470 (2011)] that, when the infected prey is permanent, there is a positive periodic orbit that is globally asymptotically stable in the interior of $(\\R^+)^3$. In this paper we prove the existence part of the conjecture.","authors_text":"C\\'esar M. Silva","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-19T22:40:34Z","title":"Existence of periodic orbits for periodic eco-epidemic models with disease in the prey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05125","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":"sha256:3b6bd16eb8a2a0f37a66dd8e962a95e745a4c10af33b08fd2d6576e7b5201146","target":"record","created_at":"2026-05-18T01:22:16Z","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":"b5755072a4834fbbe5fd977ddd24a1333001614ef87d480bcc700e662abcf5cf","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-19T22:40:34Z","title_canon_sha256":"4a001bf55040aa6b2c529f5d958a09ed94ac8da3245e6da781ecf3a284762d7a"},"schema_version":"1.0","source":{"id":"1601.05125","kind":"arxiv","version":1}},"canonical_sha256":"9d0e33a467015fbd1ebdb09bc6c5513b740c5f3739118ba6240d027380b34f30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d0e33a467015fbd1ebdb09bc6c5513b740c5f3739118ba6240d027380b34f30","first_computed_at":"2026-05-18T01:22:16.068570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:16.068570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GLpShEslRE1Th9u3It++c5qZ8lD49CkXZGCHugM6cvXl/z0vOa7GJ5MBDLixVi5CM7egTrkzjxcPYTOi4ULLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:16.069200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b6bd16eb8a2a0f37a66dd8e962a95e745a4c10af33b08fd2d6576e7b5201146","sha256:41816ae73828e85f95141cadf7dd14e13baa8143690ed8084615ee4f8cdf35ca"],"state_sha256":"ba6be1a71cfe98636238b9357d17aadd6b6cb4c9ee07086d968a4fd58b0f1eaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNqdLU3uTlUNBsRf6kstkYEWVm+hdr8zWO+Mcio72tTcnb9yCkak2jF6yp/uq6h9kyz4WtHiiMP7sRokdZIEDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:59:31.761528Z","bundle_sha256":"3db1539fda250e2acf121da8acd78b7d87a2a8d9b7e45c715eddaa5493e5c9e0"}}