{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OJGGUFXXNCJ3TIAPU5DOZ2FGV2","short_pith_number":"pith:OJGGUFXX","canonical_record":{"source":{"id":"1202.3529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-16T08:30:40Z","cross_cats_sorted":[],"title_canon_sha256":"a5860b06eb2563016622372bc42ba4b6f6d61c4843375076a484cafb69c19be7","abstract_canon_sha256":"de11ec7308d35400904acb96d1f6b4802a65de45fb362d9d457a508a0e384fe7"},"schema_version":"1.0"},"canonical_sha256":"724c6a16f76893b9a00fa746ece8a6ae85569fb350b8363798a7a3937631ec1a","source":{"kind":"arxiv","id":"1202.3529","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3529","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3529v1","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3529","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"OJGGUFXXNCJ3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJGGUFXXNCJ3TIAP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJGGUFXX","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OJGGUFXXNCJ3TIAPU5DOZ2FGV2","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-16T08:30:40Z","cross_cats_sorted":[],"title_canon_sha256":"a5860b06eb2563016622372bc42ba4b6f6d61c4843375076a484cafb69c19be7","abstract_canon_sha256":"de11ec7308d35400904acb96d1f6b4802a65de45fb362d9d457a508a0e384fe7"},"schema_version":"1.0"},"canonical_sha256":"724c6a16f76893b9a00fa746ece8a6ae85569fb350b8363798a7a3937631ec1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:22.618497Z","signature_b64":"gHodKaf5ui9GoPEFZYTFA8uKHtIyJz9gGp2/+x549Do2LOy5kZPDTu5jZFqt9hdlXT2bolEEsZP8jnaBiEsgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"724c6a16f76893b9a00fa746ece8a6ae85569fb350b8363798a7a3937631ec1a","last_reissued_at":"2026-05-18T03:12:22.617587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:22.617587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3529","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":"2026-05-18T03:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y01cRz4OetvWVjRogLbFi3CD0/3hr9TLzwyWmfc1FBQG6HhUjK1irXN4Ag2HCAC4Ua2fRCbLVziAP/LJIOq5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:54.680676Z"},"content_sha256":"486b21ceb8558efdb436c2701223ee6a228e3dcff6389d4883e38997c81ec799","schema_version":"1.0","event_id":"sha256:486b21ceb8558efdb436c2701223ee6a228e3dcff6389d4883e38997c81ec799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OJGGUFXXNCJ3TIAPU5DOZ2FGV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On positive solutions and the Omega limit set for a class of delay differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Changjing Zhuge, Jinzhi Lei, Xiaojuan Sun","submitted_at":"2012-02-16T08:30:40Z","abstract_excerpt":"This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\\leq 0$ such that the solution is positive for all time $t>0$. The condition is \"optimal\". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\\omega$ limit set of this dynamical system, which can provide informations about the long "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3529","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":"2026-05-18T03:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RRvh8b7c3vlnt79tsV5AW9h9C2DEc8prwu+mY8sizSeqzo+zgxEtJCZBNVJqb4ZQNVGJ1hcyKiBo1rj2SAiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:54.681403Z"},"content_sha256":"4100059a5548475200ce63fa1cc0ce667f80f6efe1e42d5b35ae3b52ad2cf45a","schema_version":"1.0","event_id":"sha256:4100059a5548475200ce63fa1cc0ce667f80f6efe1e42d5b35ae3b52ad2cf45a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/bundle.json","state_url":"https://pith.science/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/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":"2026-06-07T17:32:54Z","links":{"resolver":"https://pith.science/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2","bundle":"https://pith.science/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/bundle.json","state":"https://pith.science/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJGGUFXXNCJ3TIAPU5DOZ2FGV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OJGGUFXXNCJ3TIAPU5DOZ2FGV2","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":"de11ec7308d35400904acb96d1f6b4802a65de45fb362d9d457a508a0e384fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-16T08:30:40Z","title_canon_sha256":"a5860b06eb2563016622372bc42ba4b6f6d61c4843375076a484cafb69c19be7"},"schema_version":"1.0","source":{"id":"1202.3529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3529","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3529v1","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3529","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"OJGGUFXXNCJ3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJGGUFXXNCJ3TIAP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJGGUFXX","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:4100059a5548475200ce63fa1cc0ce667f80f6efe1e42d5b35ae3b52ad2cf45a","target":"graph","created_at":"2026-05-18T03:12:22Z","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":"This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\\leq 0$ such that the solution is positive for all time $t>0$. The condition is \"optimal\". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\\omega$ limit set of this dynamical system, which can provide informations about the long ","authors_text":"Changjing Zhuge, Jinzhi Lei, Xiaojuan Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-16T08:30:40Z","title":"On positive solutions and the Omega limit set for a class of delay differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3529","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":"sha256:486b21ceb8558efdb436c2701223ee6a228e3dcff6389d4883e38997c81ec799","target":"record","created_at":"2026-05-18T03:12:22Z","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":"de11ec7308d35400904acb96d1f6b4802a65de45fb362d9d457a508a0e384fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-16T08:30:40Z","title_canon_sha256":"a5860b06eb2563016622372bc42ba4b6f6d61c4843375076a484cafb69c19be7"},"schema_version":"1.0","source":{"id":"1202.3529","kind":"arxiv","version":1}},"canonical_sha256":"724c6a16f76893b9a00fa746ece8a6ae85569fb350b8363798a7a3937631ec1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"724c6a16f76893b9a00fa746ece8a6ae85569fb350b8363798a7a3937631ec1a","first_computed_at":"2026-05-18T03:12:22.617587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:22.617587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHodKaf5ui9GoPEFZYTFA8uKHtIyJz9gGp2/+x549Do2LOy5kZPDTu5jZFqt9hdlXT2bolEEsZP8jnaBiEsgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:22.618497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:486b21ceb8558efdb436c2701223ee6a228e3dcff6389d4883e38997c81ec799","sha256:4100059a5548475200ce63fa1cc0ce667f80f6efe1e42d5b35ae3b52ad2cf45a"],"state_sha256":"69abf2eb10eb42594100b4a7d362865172b7f953586c886efd74abcfc652dc29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXHFin0CLwY5RLKjru0oFaFZ3DagQ4QfSyUMyo7YY1+IeHT0085k+JKl8jmtx7ZkARi1YxKgHKysX4MSpWkMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:32:54.685112Z","bundle_sha256":"0f09cdac6a38959c1aab8fa7244639a70758fd6762a24a33063a9c06e9854f1c"}}