{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N2L7QZY77GJYVBZTY2PUMTAEP2","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":"24ec8e4dba0c6304deb29e8318bf6bf3deae7dcb7609d28be4a0358b13df622b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-03T14:40:51Z","title_canon_sha256":"9c218fb89eae7bdb7a4402d27ba6f31e38b1b1652ed3ae058cce1b0d3e65781e"},"schema_version":"1.0","source":{"id":"1409.1109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1109","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1109v1","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1109","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"N2L7QZY77GJY","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N2L7QZY77GJYVBZT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N2L7QZY7","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:9f0333043307cb75eb372a66e7e9baaf6b37018dcffeb86337872f57bfbec452","target":"graph","created_at":"2026-05-18T01:29:05Z","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":"This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows.\n  We then introduce a class of generalized perimeters, whose first variation is an admissible generalized curvature. Within this class, we implement a minimizing movements scheme and we prove that it approximates the viscosity solution of the corresponding level set PDE.\n  We also describe several exam","authors_text":"Antonin Chambolle, Marcello Ponsiglione, Massimiliano Morini","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-03T14:40:51Z","title":"Nonlocal curvature flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1109","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":"sha256:247f2eec8e9ec0ade3c8b3c36d8ee6bb26919a4559f73b2a6996f7635717affd","target":"record","created_at":"2026-05-18T01:29:05Z","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":"24ec8e4dba0c6304deb29e8318bf6bf3deae7dcb7609d28be4a0358b13df622b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-03T14:40:51Z","title_canon_sha256":"9c218fb89eae7bdb7a4402d27ba6f31e38b1b1652ed3ae058cce1b0d3e65781e"},"schema_version":"1.0","source":{"id":"1409.1109","kind":"arxiv","version":1}},"canonical_sha256":"6e97f8671ff9938a8733c69f464c047ea7c38e73ba2e858e88db5ffc9e6266d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e97f8671ff9938a8733c69f464c047ea7c38e73ba2e858e88db5ffc9e6266d5","first_computed_at":"2026-05-18T01:29:05.320649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:05.320649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kf1ub2zGNjU6cpr0xGoZUjTTkzGiLH0loOSE5fqrYkt4XM7Oh5pftOv/vGtICCNJjGZCgQ3G7VZ2DtJcr4oNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:05.321406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:247f2eec8e9ec0ade3c8b3c36d8ee6bb26919a4559f73b2a6996f7635717affd","sha256:9f0333043307cb75eb372a66e7e9baaf6b37018dcffeb86337872f57bfbec452"],"state_sha256":"3ae78fa10f0d9d9cb7676b28c8450cb20dd07f3374cf7e15156bf5c1e775da88"}