{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5T63AQO2WYFSVWD2C6SLRVFPSN","short_pith_number":"pith:5T63AQO2","canonical_record":{"source":{"id":"1902.03405","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T10:50:41Z","cross_cats_sorted":[],"title_canon_sha256":"9b5f5e1f4a5a5605a790ba209212f3b926f251f0e06513e56358817a5a3f5f4a","abstract_canon_sha256":"11f1091110ff8c1d22a355e5fed57a983985ae084f1345cdf63199f6a84a2bd8"},"schema_version":"1.0"},"canonical_sha256":"ecfdb041dab60b2ad87a17a4b8d4af935519c13a3360f0551230483bda6b6841","source":{"kind":"arxiv","id":"1902.03405","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03405","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03405v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03405","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"5T63AQO2WYFS","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5T63AQO2WYFSVWD2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5T63AQO2","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5T63AQO2WYFSVWD2C6SLRVFPSN","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03405","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T10:50:41Z","cross_cats_sorted":[],"title_canon_sha256":"9b5f5e1f4a5a5605a790ba209212f3b926f251f0e06513e56358817a5a3f5f4a","abstract_canon_sha256":"11f1091110ff8c1d22a355e5fed57a983985ae084f1345cdf63199f6a84a2bd8"},"schema_version":"1.0"},"canonical_sha256":"ecfdb041dab60b2ad87a17a4b8d4af935519c13a3360f0551230483bda6b6841","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:20.948929Z","signature_b64":"XOrp1joZhqTZTqPSClgP63m6OsodPe+1T3azmsZCar2HbWYVCYfrXIMi2SQY0/5ViPbVsFIqGhA527lIQHyECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecfdb041dab60b2ad87a17a4b8d4af935519c13a3360f0551230483bda6b6841","last_reissued_at":"2026-05-17T23:54:20.948285Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:20.948285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03405","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":"2026-05-17T23:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Tr0RTo7HFignY4YX12DAlStW8nxQnvNA3yduUSGjDPb+Bi4homwQx4L0U2Q3Gz8knE3oK4tnw87oVtiIjOUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:53:02.017836Z"},"content_sha256":"117c722611f3524c9dc09f98e91a1ae246f4d49887eb1d853a47eb324c71cd8b","schema_version":"1.0","event_id":"sha256:117c722611f3524c9dc09f98e91a1ae246f4d49887eb1d853a47eb324c71cd8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5T63AQO2WYFSVWD2C6SLRVFPSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new class of special functions arising from the solution of differential equations involving multiple proportional delays","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jayvant Patade, Sachin Bhalekar","submitted_at":"2019-02-09T10:50:41Z","abstract_excerpt":"Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of special functions is independent from all the existing special functions obtained as a solution of differential equations. We analyze the basic properties of this class and discuss various identities and relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03405","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":"2026-05-17T23:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8M8CZdH/hshr0t/B45T1BgnYOfX+TjhcS/AICf4YSDDT0HWJkkgOtnPcUJ0mFfYs9ecmVeDdWibq4yBL2/eCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:53:02.018576Z"},"content_sha256":"243aa98c72fb9b63cc07d9fc9822ff580b904d25c10196998d236acefa3267e0","schema_version":"1.0","event_id":"sha256:243aa98c72fb9b63cc07d9fc9822ff580b904d25c10196998d236acefa3267e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/bundle.json","state_url":"https://pith.science/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/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":"2026-06-10T16:53:02Z","links":{"resolver":"https://pith.science/pith/5T63AQO2WYFSVWD2C6SLRVFPSN","bundle":"https://pith.science/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/bundle.json","state":"https://pith.science/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5T63AQO2WYFSVWD2C6SLRVFPSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5T63AQO2WYFSVWD2C6SLRVFPSN","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":"11f1091110ff8c1d22a355e5fed57a983985ae084f1345cdf63199f6a84a2bd8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T10:50:41Z","title_canon_sha256":"9b5f5e1f4a5a5605a790ba209212f3b926f251f0e06513e56358817a5a3f5f4a"},"schema_version":"1.0","source":{"id":"1902.03405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03405","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03405v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03405","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"5T63AQO2WYFS","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5T63AQO2WYFSVWD2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5T63AQO2","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:243aa98c72fb9b63cc07d9fc9822ff580b904d25c10196998d236acefa3267e0","target":"graph","created_at":"2026-05-17T23:54:20Z","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":"Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of special functions is independent from all the existing special functions obtained as a solution of differential equations. We analyze the basic properties of this class and discuss various identities and relations.","authors_text":"Jayvant Patade, Sachin Bhalekar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T10:50:41Z","title":"A new class of special functions arising from the solution of differential equations involving multiple proportional delays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03405","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":"sha256:117c722611f3524c9dc09f98e91a1ae246f4d49887eb1d853a47eb324c71cd8b","target":"record","created_at":"2026-05-17T23:54:20Z","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":"11f1091110ff8c1d22a355e5fed57a983985ae084f1345cdf63199f6a84a2bd8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T10:50:41Z","title_canon_sha256":"9b5f5e1f4a5a5605a790ba209212f3b926f251f0e06513e56358817a5a3f5f4a"},"schema_version":"1.0","source":{"id":"1902.03405","kind":"arxiv","version":1}},"canonical_sha256":"ecfdb041dab60b2ad87a17a4b8d4af935519c13a3360f0551230483bda6b6841","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecfdb041dab60b2ad87a17a4b8d4af935519c13a3360f0551230483bda6b6841","first_computed_at":"2026-05-17T23:54:20.948285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:20.948285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XOrp1joZhqTZTqPSClgP63m6OsodPe+1T3azmsZCar2HbWYVCYfrXIMi2SQY0/5ViPbVsFIqGhA527lIQHyECw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:20.948929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:117c722611f3524c9dc09f98e91a1ae246f4d49887eb1d853a47eb324c71cd8b","sha256:243aa98c72fb9b63cc07d9fc9822ff580b904d25c10196998d236acefa3267e0"],"state_sha256":"8ceaa55afda26c43fed2a425d7efad28ff84d4758c100a9b5013899d4969b229"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WLqW/oRvMgVn90oUX35NPevJYgNF/WcTdvo9vQ2POq1+4Va9OK+FJEJW7uxF7IXxSrgFNr39PASkaimPY/KBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:53:02.022682Z","bundle_sha256":"857b0a7c6e64e9d10a71d7aae95b7e0b5a7eb887058b4fdf03d598646a5ca56e"}}