{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RFK6WEPTT4CMTX47FSD562C2L5","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":"b94fbde43243bf6af651abaa00917f5eff4d9927a145627b8a583b370e7c8787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-05T23:03:06Z","title_canon_sha256":"9ff0d9c616b5c208211a2c8a56fcb00079780a17e65d407245eba64ca56a2978"},"schema_version":"1.0","source":{"id":"1211.1069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1069","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1069v1","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1069","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"RFK6WEPTT4CM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RFK6WEPTT4CMTX47","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RFK6WEPT","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:310bc46d07e50f0a8c8ef9fc48c580b050a32d24c139737ecfd12b1e878e5a13","target":"graph","created_at":"2026-05-18T03:41:28Z","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 construct, on continuous $Q_1$ finite elements over Cartesian meshes, an interpolation operator that does not increase the total variation. The operator is stable in $L^1$ and exhibits second order approximation properties. With the help of it we provide improved error estimates for discrete minimizers of the total variation denoising problem and for total variation flows.","authors_text":"Abner J. Salgado, Ricardo H. Nochetto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-05T23:03:06Z","title":"A Total Variation Diminishing Interpolation Operator and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1069","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":"sha256:92d73f4eda3984d7fb39bd9c2bdab64369710d907226105dbd226668dd47e081","target":"record","created_at":"2026-05-18T03:41:28Z","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":"b94fbde43243bf6af651abaa00917f5eff4d9927a145627b8a583b370e7c8787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-05T23:03:06Z","title_canon_sha256":"9ff0d9c616b5c208211a2c8a56fcb00079780a17e65d407245eba64ca56a2978"},"schema_version":"1.0","source":{"id":"1211.1069","kind":"arxiv","version":1}},"canonical_sha256":"8955eb11f39f04c9df9f2c87df685a5f730a9348334068ee047ce95378f00980","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8955eb11f39f04c9df9f2c87df685a5f730a9348334068ee047ce95378f00980","first_computed_at":"2026-05-18T03:41:28.626572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:28.626572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8lMXjHVxMO0sdCIYRZ5NycMIguWwxhAOAPSAzEbtYXSkeJ/jkLiNhk967lW3cLiVMnPzTzc4jil86Pj+JaZ/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:28.627068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92d73f4eda3984d7fb39bd9c2bdab64369710d907226105dbd226668dd47e081","sha256:310bc46d07e50f0a8c8ef9fc48c580b050a32d24c139737ecfd12b1e878e5a13"],"state_sha256":"532a00ec3b2abbbe4ba33df1de58e0dd62fc8fd2ac0f003e14bd95b636d0fe03"}