{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BYX3COEPSTCCQPADEP6OL2DONJ","short_pith_number":"pith:BYX3COEP","canonical_record":{"source":{"id":"1707.06880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-21T13:02:00Z","cross_cats_sorted":[],"title_canon_sha256":"00138efce1b4c578286d0bdec87b482f426d7c5d6f3e201b6147594fffaeac77","abstract_canon_sha256":"d706693dfd04c6e1622e23b43073e6efe884dc214944148d85bf100a5df79237"},"schema_version":"1.0"},"canonical_sha256":"0e2fb1388f94c4283c0323fce5e86e6a4e9f8a22b4edbf27b8bc6baf2679019c","source":{"kind":"arxiv","id":"1707.06880","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06880","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06880v1","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06880","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"BYX3COEPSTCC","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BYX3COEPSTCCQPAD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BYX3COEP","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BYX3COEPSTCCQPADEP6OL2DONJ","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-21T13:02:00Z","cross_cats_sorted":[],"title_canon_sha256":"00138efce1b4c578286d0bdec87b482f426d7c5d6f3e201b6147594fffaeac77","abstract_canon_sha256":"d706693dfd04c6e1622e23b43073e6efe884dc214944148d85bf100a5df79237"},"schema_version":"1.0"},"canonical_sha256":"0e2fb1388f94c4283c0323fce5e86e6a4e9f8a22b4edbf27b8bc6baf2679019c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.279545Z","signature_b64":"QkHkSFNE1b6cVrZEDV/7sDUhnBAQeTxQ672dKNiWahn2K3sN8LXFXW7bEQHAcY5COUGFOUPnORTNbnAAEEYCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e2fb1388f94c4283c0323fce5e86e6a4e9f8a22b4edbf27b8bc6baf2679019c","last_reissued_at":"2026-05-18T00:39:51.278949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.278949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06880","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":"2026-05-18T00:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LTKNlSAmn9g+mm/m2kcZj7SgLpSXNOUBeZ/8ybgpcTyO23O0LKXkCsTZy2V2q/cvEYx9sznbRad/9UecOY9FCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:29:35.930057Z"},"content_sha256":"ad62fa2d335b719257bf8ccc5fbd2e7f76785283db4cfccb52a92c50036342c4","schema_version":"1.0","event_id":"sha256:ad62fa2d335b719257bf8ccc5fbd2e7f76785283db4cfccb52a92c50036342c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BYX3COEPSTCCQPADEP6OL2DONJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Wachsmuth, Eduardo Casas, Gerd Wachsmuth","submitted_at":"2017-07-21T13:02:00Z","abstract_excerpt":"We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in $L^1$. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in $L^1$-norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06880","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":"2026-05-18T00:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBVDGJFiHEjP0B18TmPmJ30Ard7t6R05XjwVjjkGwSw4kE7L0wflrnGJgxn6B1ElQFc68zbYxJN+rTt/lfhbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:29:35.930811Z"},"content_sha256":"081654440a1aa75eb1030a1897ce778c61faeddfe227fb8cac54a8cd964442f4","schema_version":"1.0","event_id":"sha256:081654440a1aa75eb1030a1897ce778c61faeddfe227fb8cac54a8cd964442f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYX3COEPSTCCQPADEP6OL2DONJ/bundle.json","state_url":"https://pith.science/pith/BYX3COEPSTCCQPADEP6OL2DONJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYX3COEPSTCCQPADEP6OL2DONJ/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":"2026-05-25T08:29:35Z","links":{"resolver":"https://pith.science/pith/BYX3COEPSTCCQPADEP6OL2DONJ","bundle":"https://pith.science/pith/BYX3COEPSTCCQPADEP6OL2DONJ/bundle.json","state":"https://pith.science/pith/BYX3COEPSTCCQPADEP6OL2DONJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYX3COEPSTCCQPADEP6OL2DONJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BYX3COEPSTCCQPADEP6OL2DONJ","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":"d706693dfd04c6e1622e23b43073e6efe884dc214944148d85bf100a5df79237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-21T13:02:00Z","title_canon_sha256":"00138efce1b4c578286d0bdec87b482f426d7c5d6f3e201b6147594fffaeac77"},"schema_version":"1.0","source":{"id":"1707.06880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06880","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06880v1","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06880","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"BYX3COEPSTCC","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BYX3COEPSTCCQPAD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BYX3COEP","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:081654440a1aa75eb1030a1897ce778c61faeddfe227fb8cac54a8cd964442f4","target":"graph","created_at":"2026-05-18T00:39:51Z","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 consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in $L^1$. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in $L^1$-norms.","authors_text":"Daniel Wachsmuth, Eduardo Casas, Gerd Wachsmuth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-21T13:02:00Z","title":"Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06880","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:ad62fa2d335b719257bf8ccc5fbd2e7f76785283db4cfccb52a92c50036342c4","target":"record","created_at":"2026-05-18T00:39:51Z","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":"d706693dfd04c6e1622e23b43073e6efe884dc214944148d85bf100a5df79237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-21T13:02:00Z","title_canon_sha256":"00138efce1b4c578286d0bdec87b482f426d7c5d6f3e201b6147594fffaeac77"},"schema_version":"1.0","source":{"id":"1707.06880","kind":"arxiv","version":1}},"canonical_sha256":"0e2fb1388f94c4283c0323fce5e86e6a4e9f8a22b4edbf27b8bc6baf2679019c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e2fb1388f94c4283c0323fce5e86e6a4e9f8a22b4edbf27b8bc6baf2679019c","first_computed_at":"2026-05-18T00:39:51.278949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:51.278949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QkHkSFNE1b6cVrZEDV/7sDUhnBAQeTxQ672dKNiWahn2K3sN8LXFXW7bEQHAcY5COUGFOUPnORTNbnAAEEYCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:51.279545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad62fa2d335b719257bf8ccc5fbd2e7f76785283db4cfccb52a92c50036342c4","sha256:081654440a1aa75eb1030a1897ce778c61faeddfe227fb8cac54a8cd964442f4"],"state_sha256":"bb9873b69ba8a0cfdc054f757b10ba7b459512261574fb6c9b5e1f5d9183f16c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzFlhUqwi4QUNdKT5mwqGU51TENlZ+yWNqA38HGqWU4bqn1OrXt2YFe1qyZtZ8fJPltfgkqBfFH+LJNcJMk7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:29:35.934344Z","bundle_sha256":"9ad685099ec9cf4e95edac45473e1617f2b1cc945314b2ff043845594cf35771"}}