{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CYEIPS4YQ4J5G4HZ6UYVG4PQOT","short_pith_number":"pith:CYEIPS4Y","canonical_record":{"source":{"id":"1605.06734","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-22T04:38:09Z","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"title_canon_sha256":"3b03ea475d35c8bcd68cde92c10fa151b788d8959221b117ebbd532b175871b0","abstract_canon_sha256":"b6955e00851c931fa8459a0e82d3ca99c35f07d78cbc35436e1f2b2268b32656"},"schema_version":"1.0"},"canonical_sha256":"160887cb988713d370f9f5315371f074ddcfb0d6a17a974e09496bfe0d069405","source":{"kind":"arxiv","id":"1605.06734","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06734","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06734v4","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06734","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"CYEIPS4YQ4J5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYEIPS4YQ4J5G4HZ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYEIPS4Y","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CYEIPS4YQ4J5G4HZ6UYVG4PQOT","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06734","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-22T04:38:09Z","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"title_canon_sha256":"3b03ea475d35c8bcd68cde92c10fa151b788d8959221b117ebbd532b175871b0","abstract_canon_sha256":"b6955e00851c931fa8459a0e82d3ca99c35f07d78cbc35436e1f2b2268b32656"},"schema_version":"1.0"},"canonical_sha256":"160887cb988713d370f9f5315371f074ddcfb0d6a17a974e09496bfe0d069405","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:05.923897Z","signature_b64":"73Z8RUWgNVWrpMcpRurd6yZtUVTVTqwuBd/gtdEpkYGHAXll9Iy8/Gc/KzyIp5Zqm/t/ZZ+J8KABcU+qp09UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"160887cb988713d370f9f5315371f074ddcfb0d6a17a974e09496bfe0d069405","last_reissued_at":"2026-05-18T00:25:05.923343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:05.923343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06734","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w80a5geYIEE7F0xsBbEHLU52n2IphyuSPLlApRpUn15xElacIfIDAzxlMCj548tqPC4RqaEy/y0YE6ECbHywCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:56:14.054352Z"},"content_sha256":"86dbd2680a1fa90bbd69ea194044eeb118fb10e9b0c5a7551b381f8112b2fe7d","schema_version":"1.0","event_id":"sha256:86dbd2680a1fa90bbd69ea194044eeb118fb10e9b0c5a7551b381f8112b2fe7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CYEIPS4YQ4J5G4HZ6UYVG4PQOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Basic theory of a class of linear functional differential equations with multiplication delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"primary_cat":"math.CA","authors_text":"Cheng-shi Liu","submitted_at":"2016-05-22T04:38:09Z","abstract_excerpt":"By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of linear pantograph equations. In particular, we get the complete results on the existence, uniqueness and non-uniqueness of the initial value problems at a general point for the kind of linear pantograph equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06734","kind":"arxiv","version":4},"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":"2026-05-18T00:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBwK0C/YxFTTib6LUY8bj6dmk3zmWZqTcBflHXMc1ckwaxHHimG9/6iB37TY+i5shHWHLc2xPsA/Qp/CCvwmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:56:14.054696Z"},"content_sha256":"fd1bbca3636299b20edf17b020e71bc1b3b8a203e715b2e6b3d70e8848ad8142","schema_version":"1.0","event_id":"sha256:fd1bbca3636299b20edf17b020e71bc1b3b8a203e715b2e6b3d70e8848ad8142"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/bundle.json","state_url":"https://pith.science/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/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":"2026-06-03T02:56:14Z","links":{"resolver":"https://pith.science/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT","bundle":"https://pith.science/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/bundle.json","state":"https://pith.science/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYEIPS4YQ4J5G4HZ6UYVG4PQOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CYEIPS4YQ4J5G4HZ6UYVG4PQOT","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":"b6955e00851c931fa8459a0e82d3ca99c35f07d78cbc35436e1f2b2268b32656","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-22T04:38:09Z","title_canon_sha256":"3b03ea475d35c8bcd68cde92c10fa151b788d8959221b117ebbd532b175871b0"},"schema_version":"1.0","source":{"id":"1605.06734","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06734","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06734v4","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06734","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"CYEIPS4YQ4J5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYEIPS4YQ4J5G4HZ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYEIPS4Y","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:fd1bbca3636299b20edf17b020e71bc1b3b8a203e715b2e6b3d70e8848ad8142","target":"graph","created_at":"2026-05-18T00:25:05Z","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":"By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of linear pantograph equations. In particular, we get the complete results on the existence, uniqueness and non-uniqueness of the initial value problems at a general point for the kind of linear pantograph equations.","authors_text":"Cheng-shi Liu","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-22T04:38:09Z","title":"Basic theory of a class of linear functional differential equations with multiplication delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06734","kind":"arxiv","version":4},"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":"sha256:86dbd2680a1fa90bbd69ea194044eeb118fb10e9b0c5a7551b381f8112b2fe7d","target":"record","created_at":"2026-05-18T00:25:05Z","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":"b6955e00851c931fa8459a0e82d3ca99c35f07d78cbc35436e1f2b2268b32656","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-22T04:38:09Z","title_canon_sha256":"3b03ea475d35c8bcd68cde92c10fa151b788d8959221b117ebbd532b175871b0"},"schema_version":"1.0","source":{"id":"1605.06734","kind":"arxiv","version":4}},"canonical_sha256":"160887cb988713d370f9f5315371f074ddcfb0d6a17a974e09496bfe0d069405","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"160887cb988713d370f9f5315371f074ddcfb0d6a17a974e09496bfe0d069405","first_computed_at":"2026-05-18T00:25:05.923343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:05.923343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73Z8RUWgNVWrpMcpRurd6yZtUVTVTqwuBd/gtdEpkYGHAXll9Iy8/Gc/KzyIp5Zqm/t/ZZ+J8KABcU+qp09UBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:05.923897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06734","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86dbd2680a1fa90bbd69ea194044eeb118fb10e9b0c5a7551b381f8112b2fe7d","sha256:fd1bbca3636299b20edf17b020e71bc1b3b8a203e715b2e6b3d70e8848ad8142"],"state_sha256":"6ad2862607df85cac61133b8106dd54e0a773f69dd36fca3a0568e0f32db4feb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"suG0hQkvkuWrd4LHPA8UAzayHhSiSGYmPq2FxK4s8tTt2WYXaxtHE2DEKcoKVrwlxRFzASKjdlrR3ZQY4EvhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:56:14.056659Z","bundle_sha256":"1540cea7980dbe1b4f79939a73689dcc9989176dfe06cc60fbea51d326689f92"}}