{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UW3ZHYKBWYTQETVNA6PPYVVQXY","short_pith_number":"pith:UW3ZHYKB","schema_version":"1.0","canonical_sha256":"a5b793e141b627024ead079efc56b0be224af387bdfbae7f50af01ae4a18a0ff","source":{"kind":"arxiv","id":"1308.0224","version":3},"attestation_state":"computed","paper":{"title":"Piecewise rigid curve deformation via a Finsler steepest descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Fran\\c{c}ois-Xavier Vialard (CEREMADE), Gabriel Peyr\\'e (CEREMADE), Giacomo Nardi (CEREMADE), Guillaume Charpiat (INRIA Sophia Antipolis)","submitted_at":"2013-08-01T14:37:31Z","abstract_excerpt":"This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study "},"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":"1308.0224","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-01T14:37:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c69284d1b33b936e25e86e6a53e5ef72bc95b348a09c3bb6b44771726439adf5","abstract_canon_sha256":"81f79401f289ae5dd915fbfd0eb1354c546828e07f5d2e20231daa93afb3d69d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:16.422066Z","signature_b64":"1runs8UknKDKFrnbGcQRhxO/5U2LdfcgmmsIRCra0ORTz5Rs8AV6ip1nlUFVDH5WWMuix7MWgG2linwqqPDSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5b793e141b627024ead079efc56b0be224af387bdfbae7f50af01ae4a18a0ff","last_reissued_at":"2026-05-18T01:25:16.421704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:16.421704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise rigid curve deformation via a Finsler steepest descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Fran\\c{c}ois-Xavier Vialard (CEREMADE), Gabriel Peyr\\'e (CEREMADE), Giacomo Nardi (CEREMADE), Guillaume Charpiat (INRIA Sophia Antipolis)","submitted_at":"2013-08-01T14:37:31Z","abstract_excerpt":"This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0224","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":"1308.0224","created_at":"2026-05-18T01:25:16.421758+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.0224v3","created_at":"2026-05-18T01:25:16.421758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0224","created_at":"2026-05-18T01:25:16.421758+00:00"},{"alias_kind":"pith_short_12","alias_value":"UW3ZHYKBWYTQ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UW3ZHYKBWYTQETVN","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UW3ZHYKB","created_at":"2026-05-18T12:28:02.375192+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/UW3ZHYKBWYTQETVNA6PPYVVQXY","json":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY.json","graph_json":"https://pith.science/api/pith-number/UW3ZHYKBWYTQETVNA6PPYVVQXY/graph.json","events_json":"https://pith.science/api/pith-number/UW3ZHYKBWYTQETVNA6PPYVVQXY/events.json","paper":"https://pith.science/paper/UW3ZHYKB"},"agent_actions":{"view_html":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY","download_json":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY.json","view_paper":"https://pith.science/paper/UW3ZHYKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.0224&json=true","fetch_graph":"https://pith.science/api/pith-number/UW3ZHYKBWYTQETVNA6PPYVVQXY/graph.json","fetch_events":"https://pith.science/api/pith-number/UW3ZHYKBWYTQETVNA6PPYVVQXY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY/action/storage_attestation","attest_author":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY/action/author_attestation","sign_citation":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY/action/citation_signature","submit_replication":"https://pith.science/pith/UW3ZHYKBWYTQETVNA6PPYVVQXY/action/replication_record"}},"created_at":"2026-05-18T01:25:16.421758+00:00","updated_at":"2026-05-18T01:25:16.421758+00:00"}