{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IG55VLJUBFQ5SSMKQ5U4NCIABQ","short_pith_number":"pith:IG55VLJU","canonical_record":{"source":{"id":"1812.04355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T12:30:40Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"e190e26a712ac102f3ee225e20b58b5ed762302b3b7d08157202e2779df12659","abstract_canon_sha256":"c5b9911331f64fcc37a8b500311c94ed4b6cf39e4be6c3e87d928088747aa5c0"},"schema_version":"1.0"},"canonical_sha256":"41bbdaad340961d9498a8769c689000c28e01405e9525c91ede528d032d3fea1","source":{"kind":"arxiv","id":"1812.04355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04355","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04355v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04355","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"IG55VLJUBFQ5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IG55VLJUBFQ5SSMK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IG55VLJU","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IG55VLJUBFQ5SSMKQ5U4NCIABQ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.04355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T12:30:40Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"e190e26a712ac102f3ee225e20b58b5ed762302b3b7d08157202e2779df12659","abstract_canon_sha256":"c5b9911331f64fcc37a8b500311c94ed4b6cf39e4be6c3e87d928088747aa5c0"},"schema_version":"1.0"},"canonical_sha256":"41bbdaad340961d9498a8769c689000c28e01405e9525c91ede528d032d3fea1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.449017Z","signature_b64":"FFUbfAbEcbScvYvwQJ5COaZoyluZGgGu03or09bxktFCU9HUoY1CQi1pq8mA4pwxPRIH6hWUnWzyX4CzU+OTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41bbdaad340961d9498a8769c689000c28e01405e9525c91ede528d032d3fea1","last_reissued_at":"2026-05-17T23:58:32.448240Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.448240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.04355","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPn9yt+RHuMGzo//2alEQw7E7hWa2WHWkBHsO5y8BlAKrIpcI9Lh6M1mkS9xFPuRmz9chNtGeoKGzVwrQkJXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:17:34.296520Z"},"content_sha256":"47d6e6284ddb8c71e3168983b216404c365fe98e66f0643549475d8f7c9670b7","schema_version":"1.0","event_id":"sha256:47d6e6284ddb8c71e3168983b216404c365fe98e66f0643549475d8f7c9670b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IG55VLJUBFQ5SSMKQ5U4NCIABQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex Regularization and Representer Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.OC","authors_text":"Antonin Chambolle, Claire Boyer, Fr\\'ed\\'eric de Gournay, Pierre Weiss, Vincent Duval, Yohann De Castro","submitted_at":"2018-12-11T12:30:40Z","abstract_excerpt":"We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be understood as the \\textit{atoms} of the regularizer. We then explicit that general principle by using a few popular applications. In particular, we relate it to the common wisdom that total gradient variation minimization favors the reconstruction of piecewise constant images."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04355","kind":"arxiv","version":1},"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":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Juef5dNeOw3Y1PW2YPZtIqkkojJx+R5JE41LK2LXwQJjL43A+w/05vUEDViWZ7vfpAtcEiiIqYbrok265tNoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:17:34.297158Z"},"content_sha256":"bdf42b4ce94232e7ad857405f0fd374266857b7fb21cc6135e1cc00462b9ec41","schema_version":"1.0","event_id":"sha256:bdf42b4ce94232e7ad857405f0fd374266857b7fb21cc6135e1cc00462b9ec41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/bundle.json","state_url":"https://pith.science/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/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":"2026-05-30T13:17:34Z","links":{"resolver":"https://pith.science/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ","bundle":"https://pith.science/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/bundle.json","state":"https://pith.science/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IG55VLJUBFQ5SSMKQ5U4NCIABQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IG55VLJUBFQ5SSMKQ5U4NCIABQ","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":"c5b9911331f64fcc37a8b500311c94ed4b6cf39e4be6c3e87d928088747aa5c0","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T12:30:40Z","title_canon_sha256":"e190e26a712ac102f3ee225e20b58b5ed762302b3b7d08157202e2779df12659"},"schema_version":"1.0","source":{"id":"1812.04355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04355","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04355v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04355","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"IG55VLJUBFQ5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IG55VLJUBFQ5SSMK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IG55VLJU","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:bdf42b4ce94232e7ad857405f0fd374266857b7fb21cc6135e1cc00462b9ec41","target":"graph","created_at":"2026-05-17T23:58:32Z","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 establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be understood as the \\textit{atoms} of the regularizer. We then explicit that general principle by using a few popular applications. In particular, we relate it to the common wisdom that total gradient variation minimization favors the reconstruction of piecewise constant images.","authors_text":"Antonin Chambolle, Claire Boyer, Fr\\'ed\\'eric de Gournay, Pierre Weiss, Vincent Duval, Yohann De Castro","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T12:30:40Z","title":"Convex Regularization and Representer Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04355","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":"sha256:47d6e6284ddb8c71e3168983b216404c365fe98e66f0643549475d8f7c9670b7","target":"record","created_at":"2026-05-17T23:58:32Z","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":"c5b9911331f64fcc37a8b500311c94ed4b6cf39e4be6c3e87d928088747aa5c0","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T12:30:40Z","title_canon_sha256":"e190e26a712ac102f3ee225e20b58b5ed762302b3b7d08157202e2779df12659"},"schema_version":"1.0","source":{"id":"1812.04355","kind":"arxiv","version":1}},"canonical_sha256":"41bbdaad340961d9498a8769c689000c28e01405e9525c91ede528d032d3fea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41bbdaad340961d9498a8769c689000c28e01405e9525c91ede528d032d3fea1","first_computed_at":"2026-05-17T23:58:32.448240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:32.448240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FFUbfAbEcbScvYvwQJ5COaZoyluZGgGu03or09bxktFCU9HUoY1CQi1pq8mA4pwxPRIH6hWUnWzyX4CzU+OTCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:32.449017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d6e6284ddb8c71e3168983b216404c365fe98e66f0643549475d8f7c9670b7","sha256:bdf42b4ce94232e7ad857405f0fd374266857b7fb21cc6135e1cc00462b9ec41"],"state_sha256":"69c285d5eea915d2284aded5725c6d18e41a79f70c84cdc267ec9be6c5d7b534"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2V/XDk2Qxi6kJneSVA4XFZqI+1hAUaKajwpzUJ4xuDRJTaf3txgdYSH//Y6FhVttWPElzb9eEWArgZuLeWvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:17:34.300139Z","bundle_sha256":"871f0bd0e520811615ac5a748a85a0f62b95aaefca82eead4f1c4d90148baca0"}}