{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:26VZHXDAPWMBFYMZVZ6ZSG5N73","short_pith_number":"pith:26VZHXDA","schema_version":"1.0","canonical_sha256":"d7ab93dc607d9812e199ae7d991badfee3d817ec71a85bb358e30227cacc55f3","source":{"kind":"arxiv","id":"1603.01427","version":3},"attestation_state":"computed","paper":{"title":"Splines are Universal Solutions of Linear Inverse Problems with Generalized-TV regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"John Paul Ward, Julien Fageot, Michael Unser","submitted_at":"2016-03-04T11:45:22Z","abstract_excerpt":"Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by considering more general operators than the derivative. This leads us to the definition of the generalized Beppo-Levi space M, which is further identified as the direct sum of two Banach spaces. We then prove that the minimization of the generalized total variation (gTV) over M, subject to some arbitrary (convex) consistency constraints on the l"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.01427","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-04T11:45:22Z","cross_cats_sorted":[],"title_canon_sha256":"5fcc24ce08c289b1970940190e52dce2500adeb3643951c235f594fba731558b","abstract_canon_sha256":"966e8aa7c5554c428166735a8affdbf236aaa04e09bd2ce79315d97a75aecf6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:09.950839Z","signature_b64":"6OzAo2CHDLh4qXRzLimTDMaBkGsPIv+E8gpUUJmxM9VDjSQXebTmS4bzdq3C6AEW0c+YT0eCJqKl+5BtjRn6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7ab93dc607d9812e199ae7d991badfee3d817ec71a85bb358e30227cacc55f3","last_reissued_at":"2026-05-17T23:51:09.950391Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:09.950391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splines are Universal Solutions of Linear Inverse Problems with Generalized-TV regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"John Paul Ward, Julien Fageot, Michael Unser","submitted_at":"2016-03-04T11:45:22Z","abstract_excerpt":"Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by considering more general operators than the derivative. This leads us to the definition of the generalized Beppo-Levi space M, which is further identified as the direct sum of two Banach spaces. We then prove that the minimization of the generalized total variation (gTV) over M, subject to some arbitrary (convex) consistency constraints on the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01427","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.01427","created_at":"2026-05-17T23:51:09.950476+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01427v3","created_at":"2026-05-17T23:51:09.950476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01427","created_at":"2026-05-17T23:51:09.950476+00:00"},{"alias_kind":"pith_short_12","alias_value":"26VZHXDAPWMB","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"26VZHXDAPWMBFYMZ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"26VZHXDA","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.10354","citing_title":"Energy on spheres and discreteness of minimizing measures","ref_index":47,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73","json":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73.json","graph_json":"https://pith.science/api/pith-number/26VZHXDAPWMBFYMZVZ6ZSG5N73/graph.json","events_json":"https://pith.science/api/pith-number/26VZHXDAPWMBFYMZVZ6ZSG5N73/events.json","paper":"https://pith.science/paper/26VZHXDA"},"agent_actions":{"view_html":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73","download_json":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73.json","view_paper":"https://pith.science/paper/26VZHXDA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01427&json=true","fetch_graph":"https://pith.science/api/pith-number/26VZHXDAPWMBFYMZVZ6ZSG5N73/graph.json","fetch_events":"https://pith.science/api/pith-number/26VZHXDAPWMBFYMZVZ6ZSG5N73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73/action/storage_attestation","attest_author":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73/action/author_attestation","sign_citation":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73/action/citation_signature","submit_replication":"https://pith.science/pith/26VZHXDAPWMBFYMZVZ6ZSG5N73/action/replication_record"}},"created_at":"2026-05-17T23:51:09.950476+00:00","updated_at":"2026-05-17T23:51:09.950476+00:00"}