{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZM5S4KV6AKNZ7KBSBZGKQA3M6P","short_pith_number":"pith:ZM5S4KV6","canonical_record":{"source":{"id":"1402.0319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-03T09:32:23Z","cross_cats_sorted":[],"title_canon_sha256":"131c756a0b7305b4951c262804a4be27ef0673475752388fc2837adb2ad04200","abstract_canon_sha256":"49d19fbc085ae77af50d6ce0bfe7f83359cc2adcda38191fa29d26775f1eb9fc"},"schema_version":"1.0"},"canonical_sha256":"cb3b2e2abe029b9fa8320e4ca8036cf3dd8e14855d83acaeef0bd5932e4dce85","source":{"kind":"arxiv","id":"1402.0319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0319","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0319v2","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0319","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZM5S4KV6AKNZ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZM5S4KV6AKNZ7KBS","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZM5S4KV6","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZM5S4KV6AKNZ7KBSBZGKQA3M6P","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-03T09:32:23Z","cross_cats_sorted":[],"title_canon_sha256":"131c756a0b7305b4951c262804a4be27ef0673475752388fc2837adb2ad04200","abstract_canon_sha256":"49d19fbc085ae77af50d6ce0bfe7f83359cc2adcda38191fa29d26775f1eb9fc"},"schema_version":"1.0"},"canonical_sha256":"cb3b2e2abe029b9fa8320e4ca8036cf3dd8e14855d83acaeef0bd5932e4dce85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:58.049451Z","signature_b64":"+dfC/aK5ymPhDYLYHsJtzXHClt2rmrq7prwvxbQYatkEn+90G1pSnzkLqxVyBuWNcEnB/KIuYBnx0FpkU/1AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb3b2e2abe029b9fa8320e4ca8036cf3dd8e14855d83acaeef0bd5932e4dce85","last_reissued_at":"2026-05-18T01:22:58.049014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:58.049014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0319","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohBy/jNiNpQxRQMQ/HCqj7RGZFNh+5ygZVBEkHD6GMeSqK2K3XIoqDlhsKPtFhOVKzqaVWeDPUsFCaqOpTq9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:35:07.437478Z"},"content_sha256":"69e8ce999386c24fcd102420892b090fef06246a98f08989a9c6ec0f2ad5462c","schema_version":"1.0","event_id":"sha256:69e8ce999386c24fcd102420892b090fef06246a98f08989a9c6ec0f2ad5462c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZM5S4KV6AKNZ7KBSBZGKQA3M6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional fundamental lemma and fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dariusz Idczak, Lo\\\"ic Bourdin","submitted_at":"2014-02-03T09:32:23Z","abstract_excerpt":"In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second result is based on an integral representation of functions possessing Riemann-Liouville fractional derivatives, derived in this paper too.\n  In the second part of the paper, we use the previous results to give necessary optimality conditions of Euler-Lagrange type (with boundary conditions) for fractional Bolza functionals and to prove an existence result for solutions of linear fractional boundary value problems. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0319","kind":"arxiv","version":2},"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":"2026-05-18T01:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F63K1jEr9Wt/oIhEOfoN5Iv9kr1nLr8xUUEaViIPD4Z8MRCANU9bHGebwNx9dpHRlpDaXSiJQIGgBn9WgeKtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:35:07.437820Z"},"content_sha256":"67cf40a5ece9631418b3ff5a82fd0f76a624624b6659b3251ffdade37ae36251","schema_version":"1.0","event_id":"sha256:67cf40a5ece9631418b3ff5a82fd0f76a624624b6659b3251ffdade37ae36251"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/bundle.json","state_url":"https://pith.science/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/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":"2026-06-22T03:35:07Z","links":{"resolver":"https://pith.science/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P","bundle":"https://pith.science/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/bundle.json","state":"https://pith.science/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZM5S4KV6AKNZ7KBSBZGKQA3M6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZM5S4KV6AKNZ7KBSBZGKQA3M6P","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":"49d19fbc085ae77af50d6ce0bfe7f83359cc2adcda38191fa29d26775f1eb9fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-03T09:32:23Z","title_canon_sha256":"131c756a0b7305b4951c262804a4be27ef0673475752388fc2837adb2ad04200"},"schema_version":"1.0","source":{"id":"1402.0319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0319","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0319v2","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0319","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZM5S4KV6AKNZ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZM5S4KV6AKNZ7KBS","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZM5S4KV6","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:67cf40a5ece9631418b3ff5a82fd0f76a624624b6659b3251ffdade37ae36251","target":"graph","created_at":"2026-05-18T01:22:58Z","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":"In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second result is based on an integral representation of functions possessing Riemann-Liouville fractional derivatives, derived in this paper too.\n  In the second part of the paper, we use the previous results to give necessary optimality conditions of Euler-Lagrange type (with boundary conditions) for fractional Bolza functionals and to prove an existence result for solutions of linear fractional boundary value problems. In the","authors_text":"Dariusz Idczak, Lo\\\"ic Bourdin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-03T09:32:23Z","title":"Fractional fundamental lemma and fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0319","kind":"arxiv","version":2},"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":"sha256:69e8ce999386c24fcd102420892b090fef06246a98f08989a9c6ec0f2ad5462c","target":"record","created_at":"2026-05-18T01:22:58Z","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":"49d19fbc085ae77af50d6ce0bfe7f83359cc2adcda38191fa29d26775f1eb9fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-02-03T09:32:23Z","title_canon_sha256":"131c756a0b7305b4951c262804a4be27ef0673475752388fc2837adb2ad04200"},"schema_version":"1.0","source":{"id":"1402.0319","kind":"arxiv","version":2}},"canonical_sha256":"cb3b2e2abe029b9fa8320e4ca8036cf3dd8e14855d83acaeef0bd5932e4dce85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb3b2e2abe029b9fa8320e4ca8036cf3dd8e14855d83acaeef0bd5932e4dce85","first_computed_at":"2026-05-18T01:22:58.049014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:58.049014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+dfC/aK5ymPhDYLYHsJtzXHClt2rmrq7prwvxbQYatkEn+90G1pSnzkLqxVyBuWNcEnB/KIuYBnx0FpkU/1AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:58.049451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69e8ce999386c24fcd102420892b090fef06246a98f08989a9c6ec0f2ad5462c","sha256:67cf40a5ece9631418b3ff5a82fd0f76a624624b6659b3251ffdade37ae36251"],"state_sha256":"b3304f516a6a36189de96f0b8c37fc716e765117ef2e14a978cea7933acde77c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bn3GyYyZ9Pjnd+k5up4/1DQHnmlDtlkPJDIT2ZYCmCVQpmI48bBZq/nZeSBYbvgD4PN1BzpnW0+5nrm97jFNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:35:07.439737Z","bundle_sha256":"dd8a0bfd8ddffa1241f6dc4270c581a23360b99d36b76baa2962ba71fdc29d4f"}}