{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KYKB5VEY2I6RTDGR3U5T477MI7","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":"93d74ec27bb8c887801e8bcebe45c4b105b9eb9e6b47c5b1194727546fba3914","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-31T09:44:40Z","title_canon_sha256":"e610da684ec343a2ff897d6767ba515de0546adc3a2131f06058d3d5f0b81262"},"schema_version":"1.0","source":{"id":"1003.6003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.6003","created_at":"2026-05-18T04:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1003.6003v2","created_at":"2026-05-18T04:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.6003","created_at":"2026-05-18T04:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"KYKB5VEY2I6R","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KYKB5VEY2I6RTDGR","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KYKB5VEY","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:35fdfb5ad91439678cfed92dc32450682d28ef47e7fb78d0d7bc37c0ce28a164","target":"graph","created_at":"2026-05-18T04:22:50Z","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 article we study a continuous Primal-Dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.","authors_text":"Michael Goldman (CMAP)","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-31T09:44:40Z","title":"Continuous Primal-Dual Methods for Image Processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.6003","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":"sha256:72e42d248f65efc836b13ca680e4e874e7075ada8c81e160bc6d565d1d9bd590","target":"record","created_at":"2026-05-18T04:22:50Z","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":"93d74ec27bb8c887801e8bcebe45c4b105b9eb9e6b47c5b1194727546fba3914","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-31T09:44:40Z","title_canon_sha256":"e610da684ec343a2ff897d6767ba515de0546adc3a2131f06058d3d5f0b81262"},"schema_version":"1.0","source":{"id":"1003.6003","kind":"arxiv","version":2}},"canonical_sha256":"56141ed498d23d198cd1dd3b3e7fec47c703eb1fdbd312ba3b0b114101e6fd11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56141ed498d23d198cd1dd3b3e7fec47c703eb1fdbd312ba3b0b114101e6fd11","first_computed_at":"2026-05-18T04:22:50.118164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:50.118164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWN50MNIkgGK3GqJbKlXKN/2B2WzeKcJPE02bQdpNKXMLX8LbKNtIDPDF3NaqKkgzH3uWy8lisp17M1PsZHMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:50.118718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.6003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e42d248f65efc836b13ca680e4e874e7075ada8c81e160bc6d565d1d9bd590","sha256:35fdfb5ad91439678cfed92dc32450682d28ef47e7fb78d0d7bc37c0ce28a164"],"state_sha256":"e24a61cb72694cc23a004f1e38d37d4026ae0cba992a587668c5385fe5c22537"}