{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OPEPXWN2S6TYL2G44EHSF7BNT2","short_pith_number":"pith:OPEPXWN2","canonical_record":{"source":{"id":"1208.1909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-09T13:48:02Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"1ab614c8f3de22a18edfe1613a2bb6ab507ed1d4c114d60e34640de2f7e9de0a","abstract_canon_sha256":"4b2dfb6f17534c5525d3bad635b3258f763e3e047e99bdde5f4d3f724cca43fc"},"schema_version":"1.0"},"canonical_sha256":"73c8fbd9ba97a785e8dce10f22fc2d9eb398035f18c21982690562148d420ed3","source":{"kind":"arxiv","id":"1208.1909","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1909","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1909v4","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1909","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"OPEPXWN2S6TY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OPEPXWN2S6TYL2G4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OPEPXWN2","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OPEPXWN2S6TYL2G44EHSF7BNT2","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-09T13:48:02Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"1ab614c8f3de22a18edfe1613a2bb6ab507ed1d4c114d60e34640de2f7e9de0a","abstract_canon_sha256":"4b2dfb6f17534c5525d3bad635b3258f763e3e047e99bdde5f4d3f724cca43fc"},"schema_version":"1.0"},"canonical_sha256":"73c8fbd9ba97a785e8dce10f22fc2d9eb398035f18c21982690562148d420ed3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.555624Z","signature_b64":"+5/SACyvl6IrXp2rOZFn4oPydJkQC27bWzn8SP4b1nanStbpTsZ7Ke5+cGVcD4HXZIBCvd5pdp0nf2kkXUJqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73c8fbd9ba97a785e8dce10f22fc2d9eb398035f18c21982690562148d420ed3","last_reissued_at":"2026-05-18T03:14:17.555172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.555172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1909","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcX6Q9EIFFGu2uEoaQCL+RLhRIgcJKYg+fh/+iNPTR9K79IKLro3AHnG6zGRveXBpiHGLC4xtqnY9moFZ23gAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:46:03.281583Z"},"content_sha256":"bf0b1a1499464a4867e5a2a2833eb0b0bda874893367cf3bf291ab4b6674eb4d","schema_version":"1.0","event_id":"sha256:bf0b1a1499464a4867e5a2a2833eb0b0bda874893367cf3bf291ab4b6674eb4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OPEPXWN2S6TYL2G44EHSF7BNT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit Representations of Green's Function for Linear Fractional Differential Operator with Variable Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Hyong-Chol O, Myong-Ha Kim","submitted_at":"2012-08-09T13:48:02Z","abstract_excerpt":"We provide explicit representations of Green's functions for general linear fractional differential operators with {\\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0, \\infty)$. Using the explicit representations for Green's function, we obtain explicit representations for solution of inhomogeneous fractional differential equation with variable coefficients of general type. Therefore the method of Green's function, which was developed in previous research for solution of fractional differential equation with constant coeff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1909","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kc0IStie+ZibEM048NWJTZT8GpinfViEkT/5A3R+M4rTugYleumtn50AwlAlDNGLdhSAj7FWfbDX91uX0zoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:46:03.282258Z"},"content_sha256":"f8a59686da3274abcdded5628f955242d49ef9618831a4e2177997c6dc77c795","schema_version":"1.0","event_id":"sha256:f8a59686da3274abcdded5628f955242d49ef9618831a4e2177997c6dc77c795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/bundle.json","state_url":"https://pith.science/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/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":"2026-05-27T06:46:03Z","links":{"resolver":"https://pith.science/pith/OPEPXWN2S6TYL2G44EHSF7BNT2","bundle":"https://pith.science/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/bundle.json","state":"https://pith.science/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPEPXWN2S6TYL2G44EHSF7BNT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OPEPXWN2S6TYL2G44EHSF7BNT2","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":"4b2dfb6f17534c5525d3bad635b3258f763e3e047e99bdde5f4d3f724cca43fc","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-09T13:48:02Z","title_canon_sha256":"1ab614c8f3de22a18edfe1613a2bb6ab507ed1d4c114d60e34640de2f7e9de0a"},"schema_version":"1.0","source":{"id":"1208.1909","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1909","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1909v4","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1909","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"OPEPXWN2S6TY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OPEPXWN2S6TYL2G4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OPEPXWN2","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:f8a59686da3274abcdded5628f955242d49ef9618831a4e2177997c6dc77c795","target":"graph","created_at":"2026-05-18T03:14:17Z","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":"We provide explicit representations of Green's functions for general linear fractional differential operators with {\\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0, \\infty)$. Using the explicit representations for Green's function, we obtain explicit representations for solution of inhomogeneous fractional differential equation with variable coefficients of general type. Therefore the method of Green's function, which was developed in previous research for solution of fractional differential equation with constant coeff","authors_text":"Hyong-Chol O, Myong-Ha Kim","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-09T13:48:02Z","title":"Explicit Representations of Green's Function for Linear Fractional Differential Operator with Variable Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1909","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:bf0b1a1499464a4867e5a2a2833eb0b0bda874893367cf3bf291ab4b6674eb4d","target":"record","created_at":"2026-05-18T03:14:17Z","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":"4b2dfb6f17534c5525d3bad635b3258f763e3e047e99bdde5f4d3f724cca43fc","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-09T13:48:02Z","title_canon_sha256":"1ab614c8f3de22a18edfe1613a2bb6ab507ed1d4c114d60e34640de2f7e9de0a"},"schema_version":"1.0","source":{"id":"1208.1909","kind":"arxiv","version":4}},"canonical_sha256":"73c8fbd9ba97a785e8dce10f22fc2d9eb398035f18c21982690562148d420ed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73c8fbd9ba97a785e8dce10f22fc2d9eb398035f18c21982690562148d420ed3","first_computed_at":"2026-05-18T03:14:17.555172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.555172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+5/SACyvl6IrXp2rOZFn4oPydJkQC27bWzn8SP4b1nanStbpTsZ7Ke5+cGVcD4HXZIBCvd5pdp0nf2kkXUJqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.555624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1909","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf0b1a1499464a4867e5a2a2833eb0b0bda874893367cf3bf291ab4b6674eb4d","sha256:f8a59686da3274abcdded5628f955242d49ef9618831a4e2177997c6dc77c795"],"state_sha256":"5290965dae81e14d6d2ed5c0cb0cedbbb6651de582c285d46c47e5d3d87f4266"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zdBRP5FA+jI1HPLfDypRVpOrVN5uk9j2ShkDFfzouLljlPkP37rH1dxq+MV4rU99mwW5PUyK33QVZWYUVHKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:46:03.285912Z","bundle_sha256":"b9012323ed261f4864249cc253a2c174d7c986bc437fed23107a3321f5906920"}}