{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZYQDPMLKJQC5UCSEJ57HTSDCEF","short_pith_number":"pith:ZYQDPMLK","schema_version":"1.0","canonical_sha256":"ce2037b16a4c05da0a444f7e79c8622176466faa558645c2bba84e532a70acd9","source":{"kind":"arxiv","id":"1411.3951","version":2},"attestation_state":"computed","paper":{"title":"The $L^1$ gradient flow of a generalized scale invariant Willmore energy for radially non increasing functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Dayrens (ICJ)","submitted_at":"2014-11-13T19:24:06Z","abstract_excerpt":"We use the minimizing movement theory to study the gradient flow associated with a non-regular relaxation of a geometric functional derived from the Willmore energy. Thanks to the coarea formula, one can define a Willmore energy on regular functions of L 1 (R d). This functional is extended to every L 1 function by taking its lower semi-continuous envelope. We study the flow generated by this relaxed energy for radially non-increasing functions, i.e. functions with balls as level sets. In the first part of the paper, we prove a coarea formula for the relaxed energy of such functions. Then we s"},"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":"1411.3951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-13T19:24:06Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"08c583976d867ace80d6c1db115a5cf6a0a2426ef2cd78f76911a7379d0e7925","abstract_canon_sha256":"0f0dc8f885c9a064dac3fa66d475a6ad28df952cc5afcacc60cef994442954d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:27.571883Z","signature_b64":"yrBSRbAZtHL0n6z0epQiDo3dxCqvbyz9KBsSm3RgPu4IvUtjTY8tmNWvY13kjI4Jc3ArEWvuQc9h9ExRZApqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2037b16a4c05da0a444f7e79c8622176466faa558645c2bba84e532a70acd9","last_reissued_at":"2026-05-18T01:11:27.571228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:27.571228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $L^1$ gradient flow of a generalized scale invariant Willmore energy for radially non increasing functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Dayrens (ICJ)","submitted_at":"2014-11-13T19:24:06Z","abstract_excerpt":"We use the minimizing movement theory to study the gradient flow associated with a non-regular relaxation of a geometric functional derived from the Willmore energy. Thanks to the coarea formula, one can define a Willmore energy on regular functions of L 1 (R d). This functional is extended to every L 1 function by taking its lower semi-continuous envelope. We study the flow generated by this relaxed energy for radially non-increasing functions, i.e. functions with balls as level sets. In the first part of the paper, we prove a coarea formula for the relaxed energy of such functions. Then we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3951","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":"1411.3951","created_at":"2026-05-18T01:11:27.571307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3951v2","created_at":"2026-05-18T01:11:27.571307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3951","created_at":"2026-05-18T01:11:27.571307+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYQDPMLKJQC5","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYQDPMLKJQC5UCSE","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYQDPMLK","created_at":"2026-05-18T12:28:59.999130+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/ZYQDPMLKJQC5UCSEJ57HTSDCEF","json":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF.json","graph_json":"https://pith.science/api/pith-number/ZYQDPMLKJQC5UCSEJ57HTSDCEF/graph.json","events_json":"https://pith.science/api/pith-number/ZYQDPMLKJQC5UCSEJ57HTSDCEF/events.json","paper":"https://pith.science/paper/ZYQDPMLK"},"agent_actions":{"view_html":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF","download_json":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF.json","view_paper":"https://pith.science/paper/ZYQDPMLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3951&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYQDPMLKJQC5UCSEJ57HTSDCEF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYQDPMLKJQC5UCSEJ57HTSDCEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF/action/storage_attestation","attest_author":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF/action/author_attestation","sign_citation":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF/action/citation_signature","submit_replication":"https://pith.science/pith/ZYQDPMLKJQC5UCSEJ57HTSDCEF/action/replication_record"}},"created_at":"2026-05-18T01:11:27.571307+00:00","updated_at":"2026-05-18T01:11:27.571307+00:00"}