{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MS4ZXQ46EGHV6EYWUB5E5FPTWO","short_pith_number":"pith:MS4ZXQ46","canonical_record":{"source":{"id":"1410.6718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T15:59:37Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"997959d2ef050ba3a61edd7f467d1f2c61b0bc8fde4bb45870cd01879081b09b","abstract_canon_sha256":"e08fd7613ae9bcda0cd5789d14ef013b57bf9684ccf00fd5d2cda33f837616af"},"schema_version":"1.0"},"canonical_sha256":"64b99bc39e218f5f1316a07a4e95f3b3b17e12a24d1dcad30c22bf0915b72d57","source":{"kind":"arxiv","id":"1410.6718","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6718","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6718v1","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6718","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"MS4ZXQ46EGHV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS4ZXQ46EGHV6EYW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS4ZXQ46","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MS4ZXQ46EGHV6EYWUB5E5FPTWO","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T15:59:37Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"997959d2ef050ba3a61edd7f467d1f2c61b0bc8fde4bb45870cd01879081b09b","abstract_canon_sha256":"e08fd7613ae9bcda0cd5789d14ef013b57bf9684ccf00fd5d2cda33f837616af"},"schema_version":"1.0"},"canonical_sha256":"64b99bc39e218f5f1316a07a4e95f3b3b17e12a24d1dcad30c22bf0915b72d57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:24.728620Z","signature_b64":"bzvti43fNMh10PSdDmKSyPMFOLiEl00v5xizK/9EoYsOYdjazCj1pomoUQZ/zfQRZlSWSdsMNQfoOaSekNr8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64b99bc39e218f5f1316a07a4e95f3b3b17e12a24d1dcad30c22bf0915b72d57","last_reissued_at":"2026-05-18T02:39:24.728223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:24.728223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6718","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":"2026-05-18T02:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWNdLSiR2omnHHleSK51GrdUMDSsnJFA/t6Ve34GTniFdtZWpb1q6x8oRN7efWYkf3r90gE6SHFI8O0/V15vAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:30:07.221352Z"},"content_sha256":"fba62f3e332a2f042f80e450d1b7a4b50de51901e2a1481577e3d6efd946e0b2","schema_version":"1.0","event_id":"sha256:fba62f3e332a2f042f80e450d1b7a4b50de51901e2a1481577e3d6efd946e0b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MS4ZXQ46EGHV6EYWUB5E5FPTWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control for a phase field system with a possibly singular potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Elisabetta Rocca, Gabriela Marinoschi, Gianni Gilardi, Pierluigi Colli","submitted_at":"2014-10-24T15:59:37Z","abstract_excerpt":"In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6718","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":"2026-05-18T02:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqgjeXGTPXO8OughvpAB8HFU7IaUSyICCDjfU+3iPmfkvnDPy+mJufQT6SMZfko6UaL+QsWNqW90bmec0wEsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:30:07.221720Z"},"content_sha256":"fe4052bfec342485bed7a4282beae504a3dd6e8c5413c12e0fcd3fdc8b911249","schema_version":"1.0","event_id":"sha256:fe4052bfec342485bed7a4282beae504a3dd6e8c5413c12e0fcd3fdc8b911249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/bundle.json","state_url":"https://pith.science/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/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":"2026-05-26T04:30:07Z","links":{"resolver":"https://pith.science/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO","bundle":"https://pith.science/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/bundle.json","state":"https://pith.science/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MS4ZXQ46EGHV6EYWUB5E5FPTWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MS4ZXQ46EGHV6EYWUB5E5FPTWO","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":"e08fd7613ae9bcda0cd5789d14ef013b57bf9684ccf00fd5d2cda33f837616af","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T15:59:37Z","title_canon_sha256":"997959d2ef050ba3a61edd7f467d1f2c61b0bc8fde4bb45870cd01879081b09b"},"schema_version":"1.0","source":{"id":"1410.6718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6718","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6718v1","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6718","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"MS4ZXQ46EGHV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS4ZXQ46EGHV6EYW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS4ZXQ46","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:fe4052bfec342485bed7a4282beae504a3dd6e8c5413c12e0fcd3fdc8b911249","target":"graph","created_at":"2026-05-18T02:39:24Z","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 this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions.","authors_text":"Elisabetta Rocca, Gabriela Marinoschi, Gianni Gilardi, Pierluigi Colli","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T15:59:37Z","title":"Optimal control for a phase field system with a possibly singular potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6718","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:fba62f3e332a2f042f80e450d1b7a4b50de51901e2a1481577e3d6efd946e0b2","target":"record","created_at":"2026-05-18T02:39:24Z","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":"e08fd7613ae9bcda0cd5789d14ef013b57bf9684ccf00fd5d2cda33f837616af","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T15:59:37Z","title_canon_sha256":"997959d2ef050ba3a61edd7f467d1f2c61b0bc8fde4bb45870cd01879081b09b"},"schema_version":"1.0","source":{"id":"1410.6718","kind":"arxiv","version":1}},"canonical_sha256":"64b99bc39e218f5f1316a07a4e95f3b3b17e12a24d1dcad30c22bf0915b72d57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64b99bc39e218f5f1316a07a4e95f3b3b17e12a24d1dcad30c22bf0915b72d57","first_computed_at":"2026-05-18T02:39:24.728223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:24.728223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bzvti43fNMh10PSdDmKSyPMFOLiEl00v5xizK/9EoYsOYdjazCj1pomoUQZ/zfQRZlSWSdsMNQfoOaSekNr8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:24.728620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fba62f3e332a2f042f80e450d1b7a4b50de51901e2a1481577e3d6efd946e0b2","sha256:fe4052bfec342485bed7a4282beae504a3dd6e8c5413c12e0fcd3fdc8b911249"],"state_sha256":"b8159b6965f7dbfed80131e1a27ef21a0f3ae17e63dcd0e7a3f5f6470660c7a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cpzlbMJ5XbXvGZihud0igI21zUO9Px2YftqCDGRtfiqUsbXMaZr6PQLxB5bqMv3/cTy9ugjLO9Ytn63PcNEDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:30:07.225060Z","bundle_sha256":"521553780433b25a210872ffd16b86dedd0341c39d35c748df98a75032358c1d"}}