{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4YYPEVWEFX4KX4OU575A552WZI","short_pith_number":"pith:4YYPEVWE","schema_version":"1.0","canonical_sha256":"e630f256c42df8abf1d4effa0ef756ca17ee21e6129a0ba527fb6e8d971abb77","source":{"kind":"arxiv","id":"1612.05142","version":2},"attestation_state":"computed","paper":{"title":"One dimensional fractional order $TGV$: Gamma-convergence and bilevel training scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisa Davoli, Pan Liu","submitted_at":"2016-12-15T17:07:56Z","abstract_excerpt":"New fractional $r$-order seminorms, $TGV^r$, $r\\in \\mathbb R$, $r\\geq 1$, are proposed in the one-dimensional (1D) setting, as a generalization of the integer order $TGV^k$-seminorms, $k\\in\\mathbb{N}$. The fractional $r$-order $TGV^r$-seminorms are shown to be intermediate between the integer order $TGV^k$-seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect to parameters and order of derivation is performed. Existence of solutions to the bilevel training scheme is proved by $\\Gamma$-convergence. Finally, the numerical landscap"},"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":"1612.05142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-15T17:07:56Z","cross_cats_sorted":[],"title_canon_sha256":"9c25448a9dff264e7c76b318e604244ab2f0a8e73a82979925943b6122588310","abstract_canon_sha256":"ab6bc353649d53a8eced7cb0f6264fce5782fb577fbb1a0c26300f326d28196e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:22.084452Z","signature_b64":"RDPv59rz4cT28+fffTYQDnZ2n41oUsahIB+LG3iGY81cVnvgg6m10xIloRzu+uBqLH1pPsH1KdSce9+A2zHPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e630f256c42df8abf1d4effa0ef756ca17ee21e6129a0ba527fb6e8d971abb77","last_reissued_at":"2026-05-18T00:33:22.083909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:22.083909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One dimensional fractional order $TGV$: Gamma-convergence and bilevel training scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisa Davoli, Pan Liu","submitted_at":"2016-12-15T17:07:56Z","abstract_excerpt":"New fractional $r$-order seminorms, $TGV^r$, $r\\in \\mathbb R$, $r\\geq 1$, are proposed in the one-dimensional (1D) setting, as a generalization of the integer order $TGV^k$-seminorms, $k\\in\\mathbb{N}$. The fractional $r$-order $TGV^r$-seminorms are shown to be intermediate between the integer order $TGV^k$-seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect to parameters and order of derivation is performed. Existence of solutions to the bilevel training scheme is proved by $\\Gamma$-convergence. Finally, the numerical landscap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05142","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.05142","created_at":"2026-05-18T00:33:22.083986+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05142v2","created_at":"2026-05-18T00:33:22.083986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05142","created_at":"2026-05-18T00:33:22.083986+00:00"},{"alias_kind":"pith_short_12","alias_value":"4YYPEVWEFX4K","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4YYPEVWEFX4KX4OU","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4YYPEVWE","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI","json":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI.json","graph_json":"https://pith.science/api/pith-number/4YYPEVWEFX4KX4OU575A552WZI/graph.json","events_json":"https://pith.science/api/pith-number/4YYPEVWEFX4KX4OU575A552WZI/events.json","paper":"https://pith.science/paper/4YYPEVWE"},"agent_actions":{"view_html":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI","download_json":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI.json","view_paper":"https://pith.science/paper/4YYPEVWE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05142&json=true","fetch_graph":"https://pith.science/api/pith-number/4YYPEVWEFX4KX4OU575A552WZI/graph.json","fetch_events":"https://pith.science/api/pith-number/4YYPEVWEFX4KX4OU575A552WZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI/action/storage_attestation","attest_author":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI/action/author_attestation","sign_citation":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI/action/citation_signature","submit_replication":"https://pith.science/pith/4YYPEVWEFX4KX4OU575A552WZI/action/replication_record"}},"created_at":"2026-05-18T00:33:22.083986+00:00","updated_at":"2026-05-18T00:33:22.083986+00:00"}