{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DADI7YSRU62TBE4DSH57TKPFP7","short_pith_number":"pith:DADI7YSR","schema_version":"1.0","canonical_sha256":"18068fe251a7b530938391fbf9a9e57fc7f41ab60ce167173e8c62db6d05d050","source":{"kind":"arxiv","id":"1109.6765","version":2},"attestation_state":"computed","paper":{"title":"On the gradient flow of a one-homogeneous functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Chambolle (CMAP), Ariela Briani, Giandomenico Orlandi, Matteo Novaga","submitted_at":"2011-09-30T09:16:16Z","abstract_excerpt":"We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of the Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a consequence we get existence and uniqueness of a weak solution to the Hele-Shaw flow. We also obtain an explicit representation for the Total Variation flow in one dimension and easily deduce basic quali"},"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":"1109.6765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-30T09:16:16Z","cross_cats_sorted":[],"title_canon_sha256":"f55b13814c6d6300c087271717eaec9682fca1e288d25609eb870af73966dd8b","abstract_canon_sha256":"022b4e0a1197227b70063a0a46fb074bf599c1944e460fb9bc64002025c44a95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:37.846610Z","signature_b64":"OxMSKQOZhR9WvCj+T7famBpFpMhtW/7pB6zAmNL/2v1hc5xgEDQIuWidElJ2Pd3vazQDW7lYaBSwqvYRyv+pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18068fe251a7b530938391fbf9a9e57fc7f41ab60ce167173e8c62db6d05d050","last_reissued_at":"2026-05-18T04:00:37.846000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:37.846000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the gradient flow of a one-homogeneous functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Chambolle (CMAP), Ariela Briani, Giandomenico Orlandi, Matteo Novaga","submitted_at":"2011-09-30T09:16:16Z","abstract_excerpt":"We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of the Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a consequence we get existence and uniqueness of a weak solution to the Hele-Shaw flow. We also obtain an explicit representation for the Total Variation flow in one dimension and easily deduce basic quali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6765","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":"1109.6765","created_at":"2026-05-18T04:00:37.846092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6765v2","created_at":"2026-05-18T04:00:37.846092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6765","created_at":"2026-05-18T04:00:37.846092+00:00"},{"alias_kind":"pith_short_12","alias_value":"DADI7YSRU62T","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DADI7YSRU62TBE4D","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DADI7YSR","created_at":"2026-05-18T12:26:26.731475+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/DADI7YSRU62TBE4DSH57TKPFP7","json":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7.json","graph_json":"https://pith.science/api/pith-number/DADI7YSRU62TBE4DSH57TKPFP7/graph.json","events_json":"https://pith.science/api/pith-number/DADI7YSRU62TBE4DSH57TKPFP7/events.json","paper":"https://pith.science/paper/DADI7YSR"},"agent_actions":{"view_html":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7","download_json":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7.json","view_paper":"https://pith.science/paper/DADI7YSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6765&json=true","fetch_graph":"https://pith.science/api/pith-number/DADI7YSRU62TBE4DSH57TKPFP7/graph.json","fetch_events":"https://pith.science/api/pith-number/DADI7YSRU62TBE4DSH57TKPFP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7/action/storage_attestation","attest_author":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7/action/author_attestation","sign_citation":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7/action/citation_signature","submit_replication":"https://pith.science/pith/DADI7YSRU62TBE4DSH57TKPFP7/action/replication_record"}},"created_at":"2026-05-18T04:00:37.846092+00:00","updated_at":"2026-05-18T04:00:37.846092+00:00"}