{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UXJB7JTL62DAETC342O5FDXZUT","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":"e970e0482b69d6aced70e6df5d413b57060b0336c45594d063e3677fa1a33fbe","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-10-08T19:37:18Z","title_canon_sha256":"2c5d89f3f28b8ce71e96241434e2adf22b83e9978cea0e13f098897c79659c0f"},"schema_version":"1.0","source":{"id":"1410.2228","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2228","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2228v2","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2228","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"UXJB7JTL62DA","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UXJB7JTL62DAETC3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UXJB7JTL","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:925eba50700f42683a133dea48b0b9d5e1c3a85908c9903f339e9679d22a0d63","target":"graph","created_at":"2026-05-18T02:40:46Z","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 note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.","authors_text":"Heikki Hakkarainen, Nageswari Shanmugalingam, Panu Lahti, Riikka Korte","cross_cats":["math.AP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-10-08T19:37:18Z","title":"Stability and continuity of functions of least gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2228","kind":"arxiv","version":2},"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:ba3f7027c7d3aeb0700969a5a6e6f1a1a314f90f75956aad032a6a33909e9a6c","target":"record","created_at":"2026-05-18T02:40:46Z","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":"e970e0482b69d6aced70e6df5d413b57060b0336c45594d063e3677fa1a33fbe","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-10-08T19:37:18Z","title_canon_sha256":"2c5d89f3f28b8ce71e96241434e2adf22b83e9978cea0e13f098897c79659c0f"},"schema_version":"1.0","source":{"id":"1410.2228","kind":"arxiv","version":2}},"canonical_sha256":"a5d21fa66bf686024c5be69dd28ef9a4c51ec4bfc23507dcb458db9f2d54f7c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5d21fa66bf686024c5be69dd28ef9a4c51ec4bfc23507dcb458db9f2d54f7c3","first_computed_at":"2026-05-18T02:40:46.860114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:46.860114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Dwm/lvQUWh8A7/vMB0jN9gQwideIan5iQQIUbeDvCSTDhQA0S8Zyjobs20SVr5XgXw4cGQu26h+VmidAXZ3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:46.860734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2228","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3f7027c7d3aeb0700969a5a6e6f1a1a314f90f75956aad032a6a33909e9a6c","sha256:925eba50700f42683a133dea48b0b9d5e1c3a85908c9903f339e9679d22a0d63"],"state_sha256":"be1ba4019331b6f4d77da8c7823d553287ee9ae1bd2f8394628f3629bc14d998"}