{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MJKR7IGNHFBE2TH46WOI6AJRXT","short_pith_number":"pith:MJKR7IGN","canonical_record":{"source":{"id":"1312.2351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-09T09:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"e41646f44ed401945874c6055d17b2cf88831cadef99d3164cb0cd7c8bb5c52e","abstract_canon_sha256":"e8f8fa6057d24dfbecbeb1a2fd50232f4e3d0f113aa9e9bfd85d82ec900444e5"},"schema_version":"1.0"},"canonical_sha256":"62551fa0cd39424d4cfcf59c8f0131bcdc2c0ce1b384068849940469a62acf8f","source":{"kind":"arxiv","id":"1312.2351","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2351","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2351v1","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2351","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"MJKR7IGNHFBE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MJKR7IGNHFBE2TH4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MJKR7IGN","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MJKR7IGNHFBE2TH46WOI6AJRXT","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-09T09:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"e41646f44ed401945874c6055d17b2cf88831cadef99d3164cb0cd7c8bb5c52e","abstract_canon_sha256":"e8f8fa6057d24dfbecbeb1a2fd50232f4e3d0f113aa9e9bfd85d82ec900444e5"},"schema_version":"1.0"},"canonical_sha256":"62551fa0cd39424d4cfcf59c8f0131bcdc2c0ce1b384068849940469a62acf8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:10.587381Z","signature_b64":"0fD0Z5VZmLq7yvK2lr9NnnaGe4Vs2QJHNy3iVXmGssnHMIwfUcbdEYbYYfwGi1NeuV7AblAUCEPXzaS+WuXXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62551fa0cd39424d4cfcf59c8f0131bcdc2c0ce1b384068849940469a62acf8f","last_reissued_at":"2026-05-18T03:05:10.586885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:10.586885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2351","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":"2026-05-18T03:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90AKburPGefRBI333sY92TiRUQnsalWk3UzDlTHU2T2sPYuJY1kbt5axTjEWts/Ma6646PMCt1cqlVkWHISdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:29:22.255118Z"},"content_sha256":"0f19c528ab15e14420290eaa926acae460863bd69f58d235d2f9b0840325bad1","schema_version":"1.0","event_id":"sha256:0f19c528ab15e14420290eaa926acae460863bd69f58d235d2f9b0840325bad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MJKR7IGNHFBE2TH46WOI6AJRXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control of Allen-Cahn systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christoph Rupprecht, Claudia Hecht, Josef Michl, Luise Blank, M. Hassan Farshbaf-Shaker","submitted_at":"2013-12-09T09:26:09Z","abstract_excerpt":"Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2351","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":"2026-05-18T03:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JhEutegc7w6LgMk9DwC2qelS+MlP2HCSqPb/GE/BkSzfRjYrT/W6s4IDNN3z0PywwoI9SKyBdJW/z7rC67RYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:29:22.255500Z"},"content_sha256":"5e4c7e3d34411b38b15d917b6172760d8084d38391b943a8303407c96d41993e","schema_version":"1.0","event_id":"sha256:5e4c7e3d34411b38b15d917b6172760d8084d38391b943a8303407c96d41993e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/bundle.json","state_url":"https://pith.science/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/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":"2026-05-28T01:29:22Z","links":{"resolver":"https://pith.science/pith/MJKR7IGNHFBE2TH46WOI6AJRXT","bundle":"https://pith.science/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/bundle.json","state":"https://pith.science/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJKR7IGNHFBE2TH46WOI6AJRXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MJKR7IGNHFBE2TH46WOI6AJRXT","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":"e8f8fa6057d24dfbecbeb1a2fd50232f4e3d0f113aa9e9bfd85d82ec900444e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-09T09:26:09Z","title_canon_sha256":"e41646f44ed401945874c6055d17b2cf88831cadef99d3164cb0cd7c8bb5c52e"},"schema_version":"1.0","source":{"id":"1312.2351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2351","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2351v1","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2351","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"MJKR7IGNHFBE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MJKR7IGNHFBE2TH4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MJKR7IGN","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:5e4c7e3d34411b38b15d917b6172760d8084d38391b943a8303407c96d41993e","target":"graph","created_at":"2026-05-18T03:05:10Z","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":"Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented.","authors_text":"Christoph Rupprecht, Claudia Hecht, Josef Michl, Luise Blank, M. Hassan Farshbaf-Shaker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-09T09:26:09Z","title":"Optimal control of Allen-Cahn systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2351","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":"sha256:0f19c528ab15e14420290eaa926acae460863bd69f58d235d2f9b0840325bad1","target":"record","created_at":"2026-05-18T03:05:10Z","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":"e8f8fa6057d24dfbecbeb1a2fd50232f4e3d0f113aa9e9bfd85d82ec900444e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-09T09:26:09Z","title_canon_sha256":"e41646f44ed401945874c6055d17b2cf88831cadef99d3164cb0cd7c8bb5c52e"},"schema_version":"1.0","source":{"id":"1312.2351","kind":"arxiv","version":1}},"canonical_sha256":"62551fa0cd39424d4cfcf59c8f0131bcdc2c0ce1b384068849940469a62acf8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62551fa0cd39424d4cfcf59c8f0131bcdc2c0ce1b384068849940469a62acf8f","first_computed_at":"2026-05-18T03:05:10.586885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:10.586885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fD0Z5VZmLq7yvK2lr9NnnaGe4Vs2QJHNy3iVXmGssnHMIwfUcbdEYbYYfwGi1NeuV7AblAUCEPXzaS+WuXXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:10.587381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f19c528ab15e14420290eaa926acae460863bd69f58d235d2f9b0840325bad1","sha256:5e4c7e3d34411b38b15d917b6172760d8084d38391b943a8303407c96d41993e"],"state_sha256":"162c294010cc2cc6e8069fc65b205a85ccb5646592ffaeedf6e45b9611522800"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLvNcofVw2sNtu2X92EM5W7jnPHlChRSWYszYU1vOzsfNdRx4j4FYGDnJ6dKumnCxj8Pw0YPGNIy6Kp3V71IBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:29:22.257553Z","bundle_sha256":"a7752b1028c9738af042824be15fe11ec7d90d6f84df8a28750e29958e500ba8"}}