{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AJMYYCV3LDHBXYZPBNJLNIPUQJ","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":"6e3d3c5d2501a6b87daafb5f6d121a35a57bdf2ae2ddd7b35caff8d493f83e36","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-02T18:58:25Z","title_canon_sha256":"eb97c4bc8f6639ca88c16a24cbf4a97e4e2b091646fbb2402389f8a182b470ab"},"schema_version":"1.0","source":{"id":"1305.0535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0535","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0535v1","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0535","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"AJMYYCV3LDHB","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AJMYYCV3LDHBXYZP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AJMYYCV3","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:eef6078e0721514328c75055956e691ed630628c85cae68dbf31713706f2c41c","target":"graph","created_at":"2026-05-18T03:26:39Z","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":"Motivated by problems arising in conductivity imaging, we prove existence, uniqueness, and comparison theorems - under certain sharp conditions - for minimizers of the general least gradient problem \\[\\inf_{u\\in BV_f(\\Omega)} \\int_{\\Omega}\\varphi(x,Du),\\] where $f:\\partial \\Omega\\to \\R$ is continuous, \\[ BV_f(\\Omega):=\\{v\\in BV(\\Omega): \\ \\ \\forall x\\in \\partial \\Omega, \\ \\ \\lim_{r\\to 0} \\ \\esssup_{y\\in \\Omega, |x-y|<r} |f(x) - v(y)| = 0 \\ \\} %BV_f(\\Omega)=\\{u\\in BV(\\Omega): {0.1cm} u|_{\\partial \\Omega}=f {0.1cm} \\hbox{and} {0.1cm} {0.1cm} u {0.1cm} \\hbox{is continuous at} {0.1cm} \\partial \\Om","authors_text":"Adrian I. Nachman, Amir Moradifam, Robert L. Jerrard","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-02T18:58:25Z","title":"Existence and uniqueness of minimizers of general least gradient problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0535","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":"sha256:53e49d955eaca7d2be11a5622bc3cbb1453eeaa18b6ea6ee3fc3de868c0565cf","target":"record","created_at":"2026-05-18T03:26:39Z","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":"6e3d3c5d2501a6b87daafb5f6d121a35a57bdf2ae2ddd7b35caff8d493f83e36","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-02T18:58:25Z","title_canon_sha256":"eb97c4bc8f6639ca88c16a24cbf4a97e4e2b091646fbb2402389f8a182b470ab"},"schema_version":"1.0","source":{"id":"1305.0535","kind":"arxiv","version":1}},"canonical_sha256":"02598c0abb58ce1be32f0b52b6a1f4824be4a1739b04e59b950cf696152d647a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02598c0abb58ce1be32f0b52b6a1f4824be4a1739b04e59b950cf696152d647a","first_computed_at":"2026-05-18T03:26:39.931395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:39.931395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0DPgD1hBuHCQMAJYU9y71rSRGMrG+iD2rB/0WkxOIUqKdXOLWYAMpc049O8lsLvZ1C+LlfvseQZw5059E59Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:39.932070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53e49d955eaca7d2be11a5622bc3cbb1453eeaa18b6ea6ee3fc3de868c0565cf","sha256:eef6078e0721514328c75055956e691ed630628c85cae68dbf31713706f2c41c"],"state_sha256":"3d3c9d0a5796e56976d087d51f944e5dad96668f80f3339f0c86d08f16576018"}