{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N2T4VW2TUXYFQHWPXXYMTT5526","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":"79421715bff443791ff9ba4e0fb1ee8e15f49565a88efe5184a2863a37911407","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-17T17:38:18Z","title_canon_sha256":"50208a9307bcc0e29697aae14c938686dd67b4f3cbc57cc8e456e1b2c9f48e18"},"schema_version":"1.0","source":{"id":"1310.4781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4781","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4781v1","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4781","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"pith_short_12","alias_value":"N2T4VW2TUXYF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N2T4VW2TUXYFQHWP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N2T4VW2T","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:b5b7a09db13740bfe57bb767dc96e2ea2edd199e351afee40a74baa8ddc3df91","target":"graph","created_at":"2026-05-18T03:10:12Z","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 the inverse problem of recovering a binary function from blurred and noisy data. Such problems arise in many applications, for example image processing and optimal control of PDEs. Our formulation is based on the Mumford-Shah model, but with a phase field approximation to the perimeter regularisation. We use a double obstacle potential as well as a smooth double well potential. We introduce an iterative method for solving the problem, develop a suitable discretisation of this iterative method, and prove some convergence results. Numerical simulations are presented which illustrate ","authors_text":"Andreas S. Dedner, Charles Brett, Charles M. Elliott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-17T17:38:18Z","title":"Phase field methods for binary recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4781","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:bd9ef18827754c19856843736025979d4a83ce520e6b772e2b9b95341e4fc924","target":"record","created_at":"2026-05-18T03:10:12Z","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":"79421715bff443791ff9ba4e0fb1ee8e15f49565a88efe5184a2863a37911407","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-17T17:38:18Z","title_canon_sha256":"50208a9307bcc0e29697aae14c938686dd67b4f3cbc57cc8e456e1b2c9f48e18"},"schema_version":"1.0","source":{"id":"1310.4781","kind":"arxiv","version":1}},"canonical_sha256":"6ea7cadb53a5f0581ecfbdf0c9cfbdd789c15cc745e61d45d35227d4996ba773","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ea7cadb53a5f0581ecfbdf0c9cfbdd789c15cc745e61d45d35227d4996ba773","first_computed_at":"2026-05-18T03:10:12.782713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:12.782713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7huvunpnVvsY7QrdFKQBruS3BLCc+Ht3auIZJ9Hvsx12eJPI/JAc7MMXyNVKOLDWaK0wW9e73kjQtIDdW0x9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:12.783353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd9ef18827754c19856843736025979d4a83ce520e6b772e2b9b95341e4fc924","sha256:b5b7a09db13740bfe57bb767dc96e2ea2edd199e351afee40a74baa8ddc3df91"],"state_sha256":"f58eeb8d46e39394f05162fe0c6980f750e4b3fdb6919e5f4aaa65ca667aaefc"}