{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5M5BUISRO4LZ2GC6BBZQLKOV4G","short_pith_number":"pith:5M5BUISR","canonical_record":{"source":{"id":"2411.15889","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-24T15:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"eec2f16fea73a0ecbb7877d35847a24ab221379e627579c2be31eb5e30127f4d","abstract_canon_sha256":"bdc78ed155d791a8a9912dac4a6883dd280b5c4bd4e9e90df61397a7062e6e5f"},"schema_version":"1.0"},"canonical_sha256":"eb3a1a225177179d185e087305a9d5e1a612eac02140973321be7106eb6b3aa1","source":{"kind":"arxiv","id":"2411.15889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15889","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15889v1","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15889","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"5M5BUISRO4LZ","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_16","alias_value":"5M5BUISRO4LZ2GC6","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_8","alias_value":"5M5BUISR","created_at":"2026-07-05T09:39:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5M5BUISRO4LZ2GC6BBZQLKOV4G","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15889","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-24T15:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"eec2f16fea73a0ecbb7877d35847a24ab221379e627579c2be31eb5e30127f4d","abstract_canon_sha256":"bdc78ed155d791a8a9912dac4a6883dd280b5c4bd4e9e90df61397a7062e6e5f"},"schema_version":"1.0"},"canonical_sha256":"eb3a1a225177179d185e087305a9d5e1a612eac02140973321be7106eb6b3aa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:42.886229Z","signature_b64":"mD07EYLY/Ua4tpoH8nNdK4N54OGxj6NAoj5hUxq5Mf28jNaMzYr9lElRxRS0EOnIBLixPmMZhRKpm4zV3xh1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb3a1a225177179d185e087305a9d5e1a612eac02140973321be7106eb6b3aa1","last_reissued_at":"2026-07-05T09:39:42.885755Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:42.885755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15889","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":"2026-07-05T09:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2DPakYBWrqR3VK/DBz49EQ/LQPeAtVJxCnRUgzGMEqrzrnIeFsyo66BjifYaQXcldwOT8vLYP99ITG4niRvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:33:09.786696Z"},"content_sha256":"08af801dae11d49ecee57f05ff4265cd3e6b39d3773c77edaa8feef66db4c219","schema_version":"1.0","event_id":"sha256:08af801dae11d49ecee57f05ff4265cd3e6b39d3773c77edaa8feef66db4c219"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5M5BUISRO4LZ2GC6BBZQLKOV4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further extensions on the successive approximation method for hierarchical optimal control problems and its application to learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Getachew K. Befekadu","submitted_at":"2024-11-24T15:56:25Z","abstract_excerpt":"In this paper, further extensions of the result of the paper \"A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024\" concerning a class of learning problem of point estimations for modeling of high-dimensional nonlinear functions are given. In particular, we present two viable extensions within the nested algorithm of the successive approximation method for the hierarchical optimal control problem, that provide better convergence property and computationally efficiency, which ultimately"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15889","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15889/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMmKfDQfpvyQtHVKN4TUD5QFd6D+9/tcwLvKi4+tR+M8G6vfteO5Qq+At3P73Ubi5Cy+pzgjGYGWYLG8Bv2PBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:33:09.787630Z"},"content_sha256":"936bde65625857a433bcd248690e2d9e7d9361f725f50c62fc52e1955f04477c","schema_version":"1.0","event_id":"sha256:936bde65625857a433bcd248690e2d9e7d9361f725f50c62fc52e1955f04477c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/bundle.json","state_url":"https://pith.science/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/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":"2026-08-13T01:33:09Z","links":{"resolver":"https://pith.science/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G","bundle":"https://pith.science/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/bundle.json","state":"https://pith.science/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5M5BUISRO4LZ2GC6BBZQLKOV4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5M5BUISRO4LZ2GC6BBZQLKOV4G","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":"bdc78ed155d791a8a9912dac4a6883dd280b5c4bd4e9e90df61397a7062e6e5f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-24T15:56:25Z","title_canon_sha256":"eec2f16fea73a0ecbb7877d35847a24ab221379e627579c2be31eb5e30127f4d"},"schema_version":"1.0","source":{"id":"2411.15889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15889","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15889v1","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15889","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"5M5BUISRO4LZ","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_16","alias_value":"5M5BUISRO4LZ2GC6","created_at":"2026-07-05T09:39:42Z"},{"alias_kind":"pith_short_8","alias_value":"5M5BUISR","created_at":"2026-07-05T09:39:42Z"}],"graph_snapshots":[{"event_id":"sha256:936bde65625857a433bcd248690e2d9e7d9361f725f50c62fc52e1955f04477c","target":"graph","created_at":"2026-07-05T09:39:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15889/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, further extensions of the result of the paper \"A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024\" concerning a class of learning problem of point estimations for modeling of high-dimensional nonlinear functions are given. In particular, we present two viable extensions within the nested algorithm of the successive approximation method for the hierarchical optimal control problem, that provide better convergence property and computationally efficiency, which ultimately","authors_text":"Getachew K. Befekadu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-24T15:56:25Z","title":"Further extensions on the successive approximation method for hierarchical optimal control problems and its application to learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15889","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":"sha256:08af801dae11d49ecee57f05ff4265cd3e6b39d3773c77edaa8feef66db4c219","target":"record","created_at":"2026-07-05T09:39:42Z","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":"bdc78ed155d791a8a9912dac4a6883dd280b5c4bd4e9e90df61397a7062e6e5f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-24T15:56:25Z","title_canon_sha256":"eec2f16fea73a0ecbb7877d35847a24ab221379e627579c2be31eb5e30127f4d"},"schema_version":"1.0","source":{"id":"2411.15889","kind":"arxiv","version":1}},"canonical_sha256":"eb3a1a225177179d185e087305a9d5e1a612eac02140973321be7106eb6b3aa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3a1a225177179d185e087305a9d5e1a612eac02140973321be7106eb6b3aa1","first_computed_at":"2026-07-05T09:39:42.885755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:42.885755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mD07EYLY/Ua4tpoH8nNdK4N54OGxj6NAoj5hUxq5Mf28jNaMzYr9lElRxRS0EOnIBLixPmMZhRKpm4zV3xh1Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:42.886229Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08af801dae11d49ecee57f05ff4265cd3e6b39d3773c77edaa8feef66db4c219","sha256:936bde65625857a433bcd248690e2d9e7d9361f725f50c62fc52e1955f04477c"],"state_sha256":"3bfeab3acf7c66932f9f9e408bd53305be327f1ccc8ba8e85fcc78d6164b9009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4llZncm4Fu8pZPgd1/p580MAm8mnMVxaxpF0RI5H9sE9lCuhax0dKWIC1HVLOg6zZFQ12Qr6g/ddnRp3+M7ADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:33:09.793683Z","bundle_sha256":"f6a4923ad349f5f5fcc5d967b62b9108af64c5d78bb98274fc3fd8222967ddf6"}}