{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UJXSI7WA4FURNJRHCAKTUUDZCA","short_pith_number":"pith:UJXSI7WA","canonical_record":{"source":{"id":"1504.05153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T18:45:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"516403cb69dd7aa5167fd9d6c37017ae287314b663fbf0a20ea8905babc8e98b","abstract_canon_sha256":"44a031d967d4a3f01719c5777ec52c5aa532234ea30bb793fbd320efc29f4dd6"},"schema_version":"1.0"},"canonical_sha256":"a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa","source":{"kind":"arxiv","id":"1504.05153","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05153","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05153v1","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05153","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"UJXSI7WA4FUR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UJXSI7WA4FURNJRH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UJXSI7WA","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UJXSI7WA4FURNJRHCAKTUUDZCA","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T18:45:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"516403cb69dd7aa5167fd9d6c37017ae287314b663fbf0a20ea8905babc8e98b","abstract_canon_sha256":"44a031d967d4a3f01719c5777ec52c5aa532234ea30bb793fbd320efc29f4dd6"},"schema_version":"1.0"},"canonical_sha256":"a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:57.145203Z","signature_b64":"Pn10pikch2y6Ez70r2FwEKAVLTT/QCSp/yOiV9JXq/NDD3gRSNiyE8fevUMCked2yi9wPW1BrqqnyAQdapdoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa","last_reissued_at":"2026-05-18T00:39:57.144544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:57.144544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05153","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":"2026-05-18T00:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eg/7nHOP4nk7U+fIhMK+59o3egCQ1VSDH80IJh0OSaiqOz+V5+qIeNQkjteatiHnmMK71dBNf3IYBMuKlCLdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:16:30.700016Z"},"content_sha256":"5f7053e3280c0b5a0e4d38fd5aacb45d99347814e76d0336273fcff6347c3b92","schema_version":"1.0","event_id":"sha256:5f7053e3280c0b5a0e4d38fd5aacb45d99347814e76d0336273fcff6347c3b92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UJXSI7WA4FURNJRHCAKTUUDZCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.OC","authors_text":"Amar Debbouche, Delfim F. M. Torres, Juan J. Nieto","submitted_at":"2015-04-20T18:45:39Z","abstract_excerpt":"We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05153","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":"2026-05-18T00:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SPV6ngFSEi59Vm3/LtEmWRsb7mhh87BjLYOwsAuOT/VtgocSmyvjgZcUky0dBdlKk1hI43a9W4JOunOVvSEzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:16:30.700765Z"},"content_sha256":"f1cbe8efcbf8f7b8b1f2d2fbe594f6c3b6381644c61e4811e7961e08e2ed2710","schema_version":"1.0","event_id":"sha256:f1cbe8efcbf8f7b8b1f2d2fbe594f6c3b6381644c61e4811e7961e08e2ed2710"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/bundle.json","state_url":"https://pith.science/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/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":"2026-05-28T20:16:30Z","links":{"resolver":"https://pith.science/pith/UJXSI7WA4FURNJRHCAKTUUDZCA","bundle":"https://pith.science/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/bundle.json","state":"https://pith.science/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJXSI7WA4FURNJRHCAKTUUDZCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UJXSI7WA4FURNJRHCAKTUUDZCA","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":"44a031d967d4a3f01719c5777ec52c5aa532234ea30bb793fbd320efc29f4dd6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T18:45:39Z","title_canon_sha256":"516403cb69dd7aa5167fd9d6c37017ae287314b663fbf0a20ea8905babc8e98b"},"schema_version":"1.0","source":{"id":"1504.05153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05153","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05153v1","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05153","created_at":"2026-05-18T00:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"UJXSI7WA4FUR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UJXSI7WA4FURNJRH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UJXSI7WA","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:f1cbe8efcbf8f7b8b1f2d2fbe594f6c3b6381644c61e4811e7961e08e2ed2710","target":"graph","created_at":"2026-05-18T00:39:57Z","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 introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of syste","authors_text":"Amar Debbouche, Delfim F. M. Torres, Juan J. Nieto","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T18:45:39Z","title":"Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05153","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":"sha256:5f7053e3280c0b5a0e4d38fd5aacb45d99347814e76d0336273fcff6347c3b92","target":"record","created_at":"2026-05-18T00:39:57Z","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":"44a031d967d4a3f01719c5777ec52c5aa532234ea30bb793fbd320efc29f4dd6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T18:45:39Z","title_canon_sha256":"516403cb69dd7aa5167fd9d6c37017ae287314b663fbf0a20ea8905babc8e98b"},"schema_version":"1.0","source":{"id":"1504.05153","kind":"arxiv","version":1}},"canonical_sha256":"a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa","first_computed_at":"2026-05-18T00:39:57.144544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:57.144544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pn10pikch2y6Ez70r2FwEKAVLTT/QCSp/yOiV9JXq/NDD3gRSNiyE8fevUMCked2yi9wPW1BrqqnyAQdapdoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:57.145203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f7053e3280c0b5a0e4d38fd5aacb45d99347814e76d0336273fcff6347c3b92","sha256:f1cbe8efcbf8f7b8b1f2d2fbe594f6c3b6381644c61e4811e7961e08e2ed2710"],"state_sha256":"3447192fa922959ab820ac2b5b8cd8e8422f051a4953ba2663aaf7e04421b930"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDklvIXp8pq8fwc1J/R0RttsGMC7pf3wUXhMBX+hQhJUyr3fh441piXcacSuWz1fTzBJJJI3qzBOYJ6Wx6LLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:16:30.704414Z","bundle_sha256":"4b59a5271dcfbbb452831cf9cebf9f3486db59f4e5a9507b97ba57e2df84c746"}}