{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LGWLRUJ3QB3YFFABAXKPAQPEGB","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":"c496f5ccd1100476a103c52054dd78a3202e815607712bff487d130104f3b1cb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T07:30:24Z","title_canon_sha256":"fcae3763a87b92c3142fefb174f3dae0228cbb9c693053ede69cc48df432a0d2"},"schema_version":"1.0","source":{"id":"1804.07477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07477","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07477v2","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07477","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"pith_short_12","alias_value":"LGWLRUJ3QB3Y","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LGWLRUJ3QB3YFFAB","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LGWLRUJ3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:bf2ff657217a6e4599ba9d4ba2dad3aaa12678cad4e2c7570fa38f26277c88b0","target":"graph","created_at":"2026-05-18T00:08:00Z","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":"The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is defined. DTV has favorable properties, compared to the original TV-seminorm for finite element functions. These include a convenient dual representation in terms of the supremum over the space of Raviart--Thomas finite element functions, subject to a set of simple constraints. It can therefore be shown that a variety of algorithms for classical image reconst","authors_text":"Gerd Wachsmuth, Jos\\'e Vidal-N\\'u\\~nez, Marc Herrmann, Roland Herzog, Stephan Schmidt","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T07:30:24Z","title":"Discrete Total Variation with Finite Elements and Applications to Imaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07477","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:ff786d6246bcc0102f32bf676fbcce503fd1e516d57529b697dddfb046ba7400","target":"record","created_at":"2026-05-18T00:08:00Z","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":"c496f5ccd1100476a103c52054dd78a3202e815607712bff487d130104f3b1cb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T07:30:24Z","title_canon_sha256":"fcae3763a87b92c3142fefb174f3dae0228cbb9c693053ede69cc48df432a0d2"},"schema_version":"1.0","source":{"id":"1804.07477","kind":"arxiv","version":2}},"canonical_sha256":"59acb8d13b807782940105d4f041e43047f012b3d97ecb5bd99e55ff75fcaeb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59acb8d13b807782940105d4f041e43047f012b3d97ecb5bd99e55ff75fcaeb7","first_computed_at":"2026-05-18T00:08:00.416298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:00.416298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4A1Db4MpL11kWPJfm+3S4deXfuEXHYgj7VVWO56gyKc0+avoTiktLgMRcLv4mXk0wI+jxU6M+yIuKLHWTDhAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:00.416953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff786d6246bcc0102f32bf676fbcce503fd1e516d57529b697dddfb046ba7400","sha256:bf2ff657217a6e4599ba9d4ba2dad3aaa12678cad4e2c7570fa38f26277c88b0"],"state_sha256":"9f77e2d7c1c9763ed9e1d92069e0a02465b32030b1d557d36ba481ad3e9a5631"}