{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TGJVSQPW6Z6WUU4CZGYMUJDNCV","short_pith_number":"pith:TGJVSQPW","canonical_record":{"source":{"id":"1611.03261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T11:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"a94334a96ce76d0c0c9db27ae9999a990dfd394936705bab3bc89cc32f726691","abstract_canon_sha256":"907c36cb079edbfb558d223411da98fab1663e13cca16bf0b7f96a18091d0157"},"schema_version":"1.0"},"canonical_sha256":"99935941f6f67d6a5382c9b0ca246d154a8b77248b629e59de129171273c1dc7","source":{"kind":"arxiv","id":"1611.03261","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03261","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03261v2","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03261","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"TGJVSQPW6Z6W","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TGJVSQPW6Z6WUU4C","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TGJVSQPW","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TGJVSQPW6Z6WUU4CZGYMUJDNCV","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T11:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"a94334a96ce76d0c0c9db27ae9999a990dfd394936705bab3bc89cc32f726691","abstract_canon_sha256":"907c36cb079edbfb558d223411da98fab1663e13cca16bf0b7f96a18091d0157"},"schema_version":"1.0"},"canonical_sha256":"99935941f6f67d6a5382c9b0ca246d154a8b77248b629e59de129171273c1dc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.008274Z","signature_b64":"bRFbvgyZ1ljpC6vRng7F9sVnx2zTMKK1qQjK1ygv8Yj3JIJ0SBQVyuL40KyESwVHP06Nu4UQq+luczJMr48mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99935941f6f67d6a5382c9b0ca246d154a8b77248b629e59de129171273c1dc7","last_reissued_at":"2026-05-18T00:31:29.007662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.007662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03261","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oojY60u+fpEeUZADUhrepV5TVONfPUXFF3HD2uqZXF1TbMvobZLQZg8WcgUJ234/TIDcNf2F6mEJuQNhTQzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:00:40.127975Z"},"content_sha256":"033573892ed8030d316cf3ee77dec481df5725771bf5f210cb248410c6e9a9b0","schema_version":"1.0","event_id":"sha256:033573892ed8030d316cf3ee77dec481df5725771bf5f210cb248410c6e9a9b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TGJVSQPW6Z6WUU4CZGYMUJDNCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total variation denoising in $l^1$ anisotropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Micha{\\l} {\\L}asica, Piotr B. Mucha, Salvador Moll","submitted_at":"2016-11-10T11:23:44Z","abstract_excerpt":"We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of find"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03261","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gp2K7x6ZGImTqNofKtr6Y/BYzjZGc3q2rMj0+fPTP9us2pw1b0wX71Ps6IZmtUrTN9BUxbFaz+LmhhZ0NSzfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:00:40.128345Z"},"content_sha256":"beda5e099927f2351826be7082aba920a40169445796a37cef8f7cc190955837","schema_version":"1.0","event_id":"sha256:beda5e099927f2351826be7082aba920a40169445796a37cef8f7cc190955837"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/bundle.json","state_url":"https://pith.science/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T08:00:40Z","links":{"resolver":"https://pith.science/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV","bundle":"https://pith.science/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/bundle.json","state":"https://pith.science/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGJVSQPW6Z6WUU4CZGYMUJDNCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TGJVSQPW6Z6WUU4CZGYMUJDNCV","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":"907c36cb079edbfb558d223411da98fab1663e13cca16bf0b7f96a18091d0157","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T11:23:44Z","title_canon_sha256":"a94334a96ce76d0c0c9db27ae9999a990dfd394936705bab3bc89cc32f726691"},"schema_version":"1.0","source":{"id":"1611.03261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03261","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03261v2","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03261","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"TGJVSQPW6Z6W","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TGJVSQPW6Z6WUU4C","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TGJVSQPW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:beda5e099927f2351826be7082aba920a40169445796a37cef8f7cc190955837","target":"graph","created_at":"2026-05-18T00:31:29Z","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 aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of find","authors_text":"Micha{\\l} {\\L}asica, Piotr B. Mucha, Salvador Moll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T11:23:44Z","title":"Total variation denoising in $l^1$ anisotropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03261","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":"sha256:033573892ed8030d316cf3ee77dec481df5725771bf5f210cb248410c6e9a9b0","target":"record","created_at":"2026-05-18T00:31:29Z","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":"907c36cb079edbfb558d223411da98fab1663e13cca16bf0b7f96a18091d0157","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T11:23:44Z","title_canon_sha256":"a94334a96ce76d0c0c9db27ae9999a990dfd394936705bab3bc89cc32f726691"},"schema_version":"1.0","source":{"id":"1611.03261","kind":"arxiv","version":2}},"canonical_sha256":"99935941f6f67d6a5382c9b0ca246d154a8b77248b629e59de129171273c1dc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99935941f6f67d6a5382c9b0ca246d154a8b77248b629e59de129171273c1dc7","first_computed_at":"2026-05-18T00:31:29.007662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.007662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bRFbvgyZ1ljpC6vRng7F9sVnx2zTMKK1qQjK1ygv8Yj3JIJ0SBQVyuL40KyESwVHP06Nu4UQq+luczJMr48mCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.008274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:033573892ed8030d316cf3ee77dec481df5725771bf5f210cb248410c6e9a9b0","sha256:beda5e099927f2351826be7082aba920a40169445796a37cef8f7cc190955837"],"state_sha256":"49b4f5df68b5cd34c2b5efc6638eadcc9df611343db64586ade05af355264ded"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxdd1opIkAi0bh3ghFeDi9PccgFLTzJxPcWNCshyG+uOg8xxGaSFqOtPCygxZNJxzbazqSp41CawSMZwbrR2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:00:40.130461Z","bundle_sha256":"c4b49b4a00d4bd461c76a87ffd91c14d88a9d2ad9a003ffe174a9385ebce8a83"}}