{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:COWAOHHH6MD46RYNMFV5FJ7MTS","short_pith_number":"pith:COWAOHHH","canonical_record":{"source":{"id":"1009.4684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-23T19:21:31Z","cross_cats_sorted":[],"title_canon_sha256":"7653b10165e587db7d0d9a98930ff1bf92a03c783752a2a214fc2ab9a4bede57","abstract_canon_sha256":"ecdc88835fbb2f9421b6d72b17919912dbf9b5086c9ea882ee2cf9a34f8ea392"},"schema_version":"1.0"},"canonical_sha256":"13ac071ce7f307cf470d616bd2a7ec9c9a757c12996e2d4318a23439c24d4734","source":{"kind":"arxiv","id":"1009.4684","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4684","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4684v1","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4684","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"COWAOHHH6MD4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"COWAOHHH6MD46RYN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"COWAOHHH","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:COWAOHHH6MD46RYNMFV5FJ7MTS","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-23T19:21:31Z","cross_cats_sorted":[],"title_canon_sha256":"7653b10165e587db7d0d9a98930ff1bf92a03c783752a2a214fc2ab9a4bede57","abstract_canon_sha256":"ecdc88835fbb2f9421b6d72b17919912dbf9b5086c9ea882ee2cf9a34f8ea392"},"schema_version":"1.0"},"canonical_sha256":"13ac071ce7f307cf470d616bd2a7ec9c9a757c12996e2d4318a23439c24d4734","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:21.889602Z","signature_b64":"htRcCUzNdvK8sueKUsvl03Cm40njU5ZB9O7S9rcSlro4JCSNdeP8nza2w6cbe5EElmUj73LtHTnElAfpfbFnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ac071ce7f307cf470d616bd2a7ec9c9a757c12996e2d4318a23439c24d4734","last_reissued_at":"2026-05-18T04:40:21.888933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:21.888933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4684","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":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRTAwLicz4GIC6GSTikB5A2oGahHexYpZ/fFrZ2Hb01iEfQILoqqVD9XQ7fkl+jsA1C5BRIllG63Q+Gg/CXWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:08:45.471157Z"},"content_sha256":"5d75d37e2b67feb4a9a25fae30c430ef76d7b38292fdc58c40766d3116d7331c","schema_version":"1.0","event_id":"sha256:5d75d37e2b67feb4a9a25fae30c430ef76d7b38292fdc58c40766d3116d7331c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:COWAOHHH6MD46RYNMFV5FJ7MTS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive periodic solutions of singular systems of first order ordinary differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Haiyan Wang","submitted_at":"2010-09-23T19:21:31Z","abstract_excerpt":"The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4684","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":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MrTamnBnzwZ1l6N4DtaleFD4y8sntTKRsqj/Bs/sYrxyUoPNzY887+BPuKoOTH7cVu/711MwhJrY0UkeCAC+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:08:45.471517Z"},"content_sha256":"ded60b2acaeb6bef11ce46f12f8132ee19e85a37fb9efb99289e0ba9a294cc1d","schema_version":"1.0","event_id":"sha256:ded60b2acaeb6bef11ce46f12f8132ee19e85a37fb9efb99289e0ba9a294cc1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/bundle.json","state_url":"https://pith.science/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/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":"2026-05-30T20:08:45Z","links":{"resolver":"https://pith.science/pith/COWAOHHH6MD46RYNMFV5FJ7MTS","bundle":"https://pith.science/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/bundle.json","state":"https://pith.science/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COWAOHHH6MD46RYNMFV5FJ7MTS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:COWAOHHH6MD46RYNMFV5FJ7MTS","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":"ecdc88835fbb2f9421b6d72b17919912dbf9b5086c9ea882ee2cf9a34f8ea392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-23T19:21:31Z","title_canon_sha256":"7653b10165e587db7d0d9a98930ff1bf92a03c783752a2a214fc2ab9a4bede57"},"schema_version":"1.0","source":{"id":"1009.4684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4684","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4684v1","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4684","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"COWAOHHH6MD4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"COWAOHHH6MD46RYN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"COWAOHHH","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ded60b2acaeb6bef11ce46f12f8132ee19e85a37fb9efb99289e0ba9a294cc1d","target":"graph","created_at":"2026-05-18T04:40:21Z","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":"The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone.","authors_text":"Haiyan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-23T19:21:31Z","title":"Positive periodic solutions of singular systems of first order ordinary differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4684","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":"sha256:5d75d37e2b67feb4a9a25fae30c430ef76d7b38292fdc58c40766d3116d7331c","target":"record","created_at":"2026-05-18T04:40:21Z","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":"ecdc88835fbb2f9421b6d72b17919912dbf9b5086c9ea882ee2cf9a34f8ea392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-23T19:21:31Z","title_canon_sha256":"7653b10165e587db7d0d9a98930ff1bf92a03c783752a2a214fc2ab9a4bede57"},"schema_version":"1.0","source":{"id":"1009.4684","kind":"arxiv","version":1}},"canonical_sha256":"13ac071ce7f307cf470d616bd2a7ec9c9a757c12996e2d4318a23439c24d4734","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13ac071ce7f307cf470d616bd2a7ec9c9a757c12996e2d4318a23439c24d4734","first_computed_at":"2026-05-18T04:40:21.888933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:21.888933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"htRcCUzNdvK8sueKUsvl03Cm40njU5ZB9O7S9rcSlro4JCSNdeP8nza2w6cbe5EElmUj73LtHTnElAfpfbFnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:21.889602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d75d37e2b67feb4a9a25fae30c430ef76d7b38292fdc58c40766d3116d7331c","sha256:ded60b2acaeb6bef11ce46f12f8132ee19e85a37fb9efb99289e0ba9a294cc1d"],"state_sha256":"e2c6e2dfc4357a622b35e780273131c996698badc7d07ccc63311b97ca984838"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeMrjz8T1AlG3AUIqyImMjwY7Obl7DuXnhvADvfjDwpoA5i46O1dOY49E43KiNsFKUDPnlVOixaz+8SaoFTDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:08:45.473539Z","bundle_sha256":"ff6f935f0465b223793c08ba5017186b275ba58f5019394871dfe0a71a74f052"}}