{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MZVI7VCVRRAFVC4KOJO7PDQQFW","short_pith_number":"pith:MZVI7VCV","schema_version":"1.0","canonical_sha256":"666a8fd4558c405a8b8a725df78e102dae090c43a1fb2b1fda1c15d196c4e286","source":{"kind":"arxiv","id":"1710.00798","version":2},"attestation_state":"computed","paper":{"title":"Measure-Valued Variational Models with Applications to Diffusion-Weighted Imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jan Lellmann, Thomas Vogt","submitted_at":"2017-10-02T17:11:26Z","abstract_excerpt":"We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation seminorm for functions taking values in a Banach space. The seminorm penalizes jumps and is rotationally invariant under certain conditions. We prove existence of a minimizer for a class of variational problems based on this formulation of total variation, and provide an example where uniqueness fails to hold. Employing the Kan\\-torovich-Rubinstein transport norm"},"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":"1710.00798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-02T17:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"f8dce7cf3545c62cd4803c657f0e919746a481189e83a7240663bb18eba29db0","abstract_canon_sha256":"f9191c0d0652682715178b8c2b72db94f4f8a206fa5ec44b4629727003f0409c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:47.500122Z","signature_b64":"Yuyy1tVgNOHyNjVDYzPF41xQbRLORgo5T4hHAhcrgc+0wufVYBfkUQ1W6IgvcSn+UwLQ8zwKM3VWasTig8jYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"666a8fd4558c405a8b8a725df78e102dae090c43a1fb2b1fda1c15d196c4e286","last_reissued_at":"2026-05-18T00:13:47.499543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:47.499543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measure-Valued Variational Models with Applications to Diffusion-Weighted Imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jan Lellmann, Thomas Vogt","submitted_at":"2017-10-02T17:11:26Z","abstract_excerpt":"We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation seminorm for functions taking values in a Banach space. The seminorm penalizes jumps and is rotationally invariant under certain conditions. We prove existence of a minimizer for a class of variational problems based on this formulation of total variation, and provide an example where uniqueness fails to hold. Employing the Kan\\-torovich-Rubinstein transport norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00798","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":"1710.00798","created_at":"2026-05-18T00:13:47.499622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00798v2","created_at":"2026-05-18T00:13:47.499622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00798","created_at":"2026-05-18T00:13:47.499622+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZVI7VCVRRAF","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZVI7VCVRRAFVC4K","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZVI7VCV","created_at":"2026-05-18T12:31:31.346846+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/MZVI7VCVRRAFVC4KOJO7PDQQFW","json":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW.json","graph_json":"https://pith.science/api/pith-number/MZVI7VCVRRAFVC4KOJO7PDQQFW/graph.json","events_json":"https://pith.science/api/pith-number/MZVI7VCVRRAFVC4KOJO7PDQQFW/events.json","paper":"https://pith.science/paper/MZVI7VCV"},"agent_actions":{"view_html":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW","download_json":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW.json","view_paper":"https://pith.science/paper/MZVI7VCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00798&json=true","fetch_graph":"https://pith.science/api/pith-number/MZVI7VCVRRAFVC4KOJO7PDQQFW/graph.json","fetch_events":"https://pith.science/api/pith-number/MZVI7VCVRRAFVC4KOJO7PDQQFW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW/action/storage_attestation","attest_author":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW/action/author_attestation","sign_citation":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW/action/citation_signature","submit_replication":"https://pith.science/pith/MZVI7VCVRRAFVC4KOJO7PDQQFW/action/replication_record"}},"created_at":"2026-05-18T00:13:47.499622+00:00","updated_at":"2026-05-18T00:13:47.499622+00:00"}