{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GT3A6SLPD2VROPC5INKTVNZNB4","short_pith_number":"pith:GT3A6SLP","canonical_record":{"source":{"id":"1701.08962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-31T09:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"3f51aeeddc7371ccdde741510eeef1de2950be1b5969f269196472bf5134237e","abstract_canon_sha256":"0d32e48954f59fe3da793d2681541306458d2a6c3bd6a544e3314a4244b75b40"},"schema_version":"1.0"},"canonical_sha256":"34f60f496f1eab173c5d43553ab72d0f2696c19622d5a903bd473ad317d780de","source":{"kind":"arxiv","id":"1701.08962","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08962","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08962v1","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08962","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"GT3A6SLPD2VR","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GT3A6SLPD2VROPC5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GT3A6SLP","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GT3A6SLPD2VROPC5INKTVNZNB4","target":"record","payload":{"canonical_record":{"source":{"id":"1701.08962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-31T09:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"3f51aeeddc7371ccdde741510eeef1de2950be1b5969f269196472bf5134237e","abstract_canon_sha256":"0d32e48954f59fe3da793d2681541306458d2a6c3bd6a544e3314a4244b75b40"},"schema_version":"1.0"},"canonical_sha256":"34f60f496f1eab173c5d43553ab72d0f2696c19622d5a903bd473ad317d780de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:43.937043Z","signature_b64":"A/EAijsRTiu1U8myoS3Z7DiG/tE7KBDLFJYlC1/+NdnclZ+1c/CH+8GLz2ZdY0kEKig7mygyzFAZnI8w28aeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34f60f496f1eab173c5d43553ab72d0f2696c19622d5a903bd473ad317d780de","last_reissued_at":"2026-05-18T00:42:43.936177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:43.936177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.08962","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":"2026-05-18T00:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NUabMEG/IobrnkQ8Kmy2NIkC1j1WylLWGifUcVqHioTUPSe2kXOzmKA4POQ4kvDIztrHJ5a50m0i28kJYxrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:43:06.541525Z"},"content_sha256":"36ed2e2594f0917149177fdcce07580af0007e3b8a4736e0bff40a80c7103888","schema_version":"1.0","event_id":"sha256:36ed2e2594f0917149177fdcce07580af0007e3b8a4736e0bff40a80c7103888"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GT3A6SLPD2VROPC5INKTVNZNB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Fractional Oscillator Equation with Natural Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Assia Guezane-Lakoud, Delfim F. M. Torres, Rabah Khaldi","submitted_at":"2017-01-31T09:41:52Z","abstract_excerpt":"We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the problem into an equivalent lower order fractional boundary value problem followed by the use of an upper and lower solutions method. To succeed with such approach, we first prove a result on the monotonicity of the right Caputo derivative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08962","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":"2026-05-18T00:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NynH6fctuQFWEM+PMZREyAU0nvJ2ptb4FdgFqDcrFC/ZUsjGmQSJ2r0XTnGkLgxw2HJg2Gx5AorRn2GLEmzcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:43:06.541869Z"},"content_sha256":"81528905add652e2922b3405512b11da28424da0a34aa745deb75d539ff4b360","schema_version":"1.0","event_id":"sha256:81528905add652e2922b3405512b11da28424da0a34aa745deb75d539ff4b360"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GT3A6SLPD2VROPC5INKTVNZNB4/bundle.json","state_url":"https://pith.science/pith/GT3A6SLPD2VROPC5INKTVNZNB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GT3A6SLPD2VROPC5INKTVNZNB4/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":"2026-06-26T10:43:06Z","links":{"resolver":"https://pith.science/pith/GT3A6SLPD2VROPC5INKTVNZNB4","bundle":"https://pith.science/pith/GT3A6SLPD2VROPC5INKTVNZNB4/bundle.json","state":"https://pith.science/pith/GT3A6SLPD2VROPC5INKTVNZNB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GT3A6SLPD2VROPC5INKTVNZNB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GT3A6SLPD2VROPC5INKTVNZNB4","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":"0d32e48954f59fe3da793d2681541306458d2a6c3bd6a544e3314a4244b75b40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-31T09:41:52Z","title_canon_sha256":"3f51aeeddc7371ccdde741510eeef1de2950be1b5969f269196472bf5134237e"},"schema_version":"1.0","source":{"id":"1701.08962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08962","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08962v1","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08962","created_at":"2026-05-18T00:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"GT3A6SLPD2VR","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GT3A6SLPD2VROPC5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GT3A6SLP","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:81528905add652e2922b3405512b11da28424da0a34aa745deb75d539ff4b360","target":"graph","created_at":"2026-05-18T00:42:43Z","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 prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the problem into an equivalent lower order fractional boundary value problem followed by the use of an upper and lower solutions method. To succeed with such approach, we first prove a result on the monotonicity of the right Caputo derivative.","authors_text":"Assia Guezane-Lakoud, Delfim F. M. Torres, Rabah Khaldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-31T09:41:52Z","title":"On a Fractional Oscillator Equation with Natural Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08962","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":"sha256:36ed2e2594f0917149177fdcce07580af0007e3b8a4736e0bff40a80c7103888","target":"record","created_at":"2026-05-18T00:42:43Z","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":"0d32e48954f59fe3da793d2681541306458d2a6c3bd6a544e3314a4244b75b40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-31T09:41:52Z","title_canon_sha256":"3f51aeeddc7371ccdde741510eeef1de2950be1b5969f269196472bf5134237e"},"schema_version":"1.0","source":{"id":"1701.08962","kind":"arxiv","version":1}},"canonical_sha256":"34f60f496f1eab173c5d43553ab72d0f2696c19622d5a903bd473ad317d780de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34f60f496f1eab173c5d43553ab72d0f2696c19622d5a903bd473ad317d780de","first_computed_at":"2026-05-18T00:42:43.936177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:43.936177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/EAijsRTiu1U8myoS3Z7DiG/tE7KBDLFJYlC1/+NdnclZ+1c/CH+8GLz2ZdY0kEKig7mygyzFAZnI8w28aeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:43.937043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ed2e2594f0917149177fdcce07580af0007e3b8a4736e0bff40a80c7103888","sha256:81528905add652e2922b3405512b11da28424da0a34aa745deb75d539ff4b360"],"state_sha256":"5de4f55e9f5f20df6d3c00732a265af08e915721af60a7ebd37cf3c86f3e963e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rf5ieL8q1jifxe8AqvXHJPVp6oAr7+C6Ib0DdlsZJuxlNUhfc3lBaz5bzAQZEFA6hux5MGV1MqyzwjAMRKQoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:43:06.543759Z","bundle_sha256":"49a37d64041a1db924d099b46daeef0e6b081462d1f78ceee890ed2eedca529f"}}