{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H7BESAC6C43N7AS3KDKQFYU622","short_pith_number":"pith:H7BESAC6","canonical_record":{"source":{"id":"1705.02098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-05T06:29:53Z","cross_cats_sorted":[],"title_canon_sha256":"723f53d030a81cc08d5bf3e3a55c7f32606a991304bf84dd0018e0c58561652f","abstract_canon_sha256":"c5242719ac95c4544b3ae8a0cca371a64d62c882269ddd01654b33e3b76504fd"},"schema_version":"1.0"},"canonical_sha256":"3fc249005e1736df825b50d502e29ed6aef46ada195dd3284ef164eabe1365c8","source":{"kind":"arxiv","id":"1705.02098","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02098","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02098v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02098","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"H7BESAC6C43N","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H7BESAC6C43N7AS3","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H7BESAC6","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H7BESAC6C43N7AS3KDKQFYU622","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-05T06:29:53Z","cross_cats_sorted":[],"title_canon_sha256":"723f53d030a81cc08d5bf3e3a55c7f32606a991304bf84dd0018e0c58561652f","abstract_canon_sha256":"c5242719ac95c4544b3ae8a0cca371a64d62c882269ddd01654b33e3b76504fd"},"schema_version":"1.0"},"canonical_sha256":"3fc249005e1736df825b50d502e29ed6aef46ada195dd3284ef164eabe1365c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:00.629940Z","signature_b64":"jceI2CvC5dULdt6CwDwJHnih7SbCcAJgW9/iGjAEjZ8HIKRnknY5HgMOISo98l5ihAp11/Iod42DCB6vYpTTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fc249005e1736df825b50d502e29ed6aef46ada195dd3284ef164eabe1365c8","last_reissued_at":"2026-05-18T00:45:00.629385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:00.629385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02098","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRX1T0VWcNrjlkNdeo/X4E/5rmjViAgGblkeasfPHIMYLzoTi3/K4twkwQejwY9x06DtwJ74EUKlTx7ocOhHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:12:36.896789Z"},"content_sha256":"492d7485157b4e1df3876d5d68e030a5729dd196d1cfbd31a8d889ea33951833","schema_version":"1.0","event_id":"sha256:492d7485157b4e1df3876d5d68e030a5729dd196d1cfbd31a8d889ea33951833"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H7BESAC6C43N7AS3KDKQFYU622","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of smooth solutions of multi-term Caputo-type fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Chung-Sik Sin, Gang-Il Ri, Mun-Chol KiM, Shusen Cheng","submitted_at":"2017-05-05T06:29:53Z","abstract_excerpt":"This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02098","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cYyivU1TtNbh0JMG8LKEPCGiXLgiboP0EeDhOhBkvILEUGc5rWzHmzTpmbmnLK+8hroveIvSzZASBVkwle9XCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:12:36.897140Z"},"content_sha256":"23e7db17bdfea59b57064f117188f8fd2df394038437163d82de45ecdfeb8f20","schema_version":"1.0","event_id":"sha256:23e7db17bdfea59b57064f117188f8fd2df394038437163d82de45ecdfeb8f20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H7BESAC6C43N7AS3KDKQFYU622/bundle.json","state_url":"https://pith.science/pith/H7BESAC6C43N7AS3KDKQFYU622/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H7BESAC6C43N7AS3KDKQFYU622/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":"2026-06-26T20:12:36Z","links":{"resolver":"https://pith.science/pith/H7BESAC6C43N7AS3KDKQFYU622","bundle":"https://pith.science/pith/H7BESAC6C43N7AS3KDKQFYU622/bundle.json","state":"https://pith.science/pith/H7BESAC6C43N7AS3KDKQFYU622/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H7BESAC6C43N7AS3KDKQFYU622/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H7BESAC6C43N7AS3KDKQFYU622","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":"c5242719ac95c4544b3ae8a0cca371a64d62c882269ddd01654b33e3b76504fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-05T06:29:53Z","title_canon_sha256":"723f53d030a81cc08d5bf3e3a55c7f32606a991304bf84dd0018e0c58561652f"},"schema_version":"1.0","source":{"id":"1705.02098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02098","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02098v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02098","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"H7BESAC6C43N","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H7BESAC6C43N7AS3","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H7BESAC6","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:23e7db17bdfea59b57064f117188f8fd2df394038437163d82de45ecdfeb8f20","target":"graph","created_at":"2026-05-18T00:45:00Z","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 deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.","authors_text":"Chung-Sik Sin, Gang-Il Ri, Mun-Chol KiM, Shusen Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-05T06:29:53Z","title":"Existence of smooth solutions of multi-term Caputo-type fractional differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02098","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":"sha256:492d7485157b4e1df3876d5d68e030a5729dd196d1cfbd31a8d889ea33951833","target":"record","created_at":"2026-05-18T00:45:00Z","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":"c5242719ac95c4544b3ae8a0cca371a64d62c882269ddd01654b33e3b76504fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-05T06:29:53Z","title_canon_sha256":"723f53d030a81cc08d5bf3e3a55c7f32606a991304bf84dd0018e0c58561652f"},"schema_version":"1.0","source":{"id":"1705.02098","kind":"arxiv","version":1}},"canonical_sha256":"3fc249005e1736df825b50d502e29ed6aef46ada195dd3284ef164eabe1365c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fc249005e1736df825b50d502e29ed6aef46ada195dd3284ef164eabe1365c8","first_computed_at":"2026-05-18T00:45:00.629385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:00.629385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jceI2CvC5dULdt6CwDwJHnih7SbCcAJgW9/iGjAEjZ8HIKRnknY5HgMOISo98l5ihAp11/Iod42DCB6vYpTTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:00.629940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:492d7485157b4e1df3876d5d68e030a5729dd196d1cfbd31a8d889ea33951833","sha256:23e7db17bdfea59b57064f117188f8fd2df394038437163d82de45ecdfeb8f20"],"state_sha256":"e6c2c3f975fa4cfce8d2583e58a453812d70b2f0c9dd1784ee300231af134687"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8ZNb9M6JCeeSot64QCDNjNJPErFwyVgJV3JrCMJtYwOcShnBeMAHbq2F7ezRJtEZPGUCTGAD7fvTipcbzExDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:12:36.899029Z","bundle_sha256":"109a36853d3ae4c29ec8b8149980a6b2a6739fff745bc0ed1563f2ae3a08b28c"}}