{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AFQRW5KXERGAG24WXGDVUNRAXT","short_pith_number":"pith:AFQRW5KX","schema_version":"1.0","canonical_sha256":"01611b7557244c036b96b9875a3620bcd44306578e6232ca8c29df91f888f196","source":{"kind":"arxiv","id":"1101.0777","version":1},"attestation_state":"computed","paper":{"title":"On a linear programming approach to the discrete Willmore boundary value problem and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"cs.CG","authors_text":"Daniel Cremers, Simon Masnou, Thomas Schoenemann","submitted_at":"2011-01-04T17:59:52Z","abstract_excerpt":"We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we consider a fairly general class of energies, our main focus is on the Willmore energy, i.e. the total squared mean curvature Our purpose is to address the delicate task of approximating global minimizers of the energy under boundary constraints.\n  The main contribution of this work is to translate the nonlinear boundary value problem into an integer linear "},"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":"1101.0777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-01-04T17:59:52Z","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"title_canon_sha256":"aaaada9bc0610c4cd5a186f9dc5d8e817c421a10cd0198580ad79c0fe3b47189","abstract_canon_sha256":"89cce7a35ca6fbb0207550646d78622deecb677f80155c09d124f8594dc66896"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:02.123074Z","signature_b64":"ROogMsOxrRHQS15JREb6PovJ6JLX1x7/U1ZXtNJn8UShB7Hn2i3dmXIZIYz17JVAc2VnSFKQLySfnzhn1muSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01611b7557244c036b96b9875a3620bcd44306578e6232ca8c29df91f888f196","last_reissued_at":"2026-05-18T04:32:02.122462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:02.122462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a linear programming approach to the discrete Willmore boundary value problem and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"cs.CG","authors_text":"Daniel Cremers, Simon Masnou, Thomas Schoenemann","submitted_at":"2011-01-04T17:59:52Z","abstract_excerpt":"We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we consider a fairly general class of energies, our main focus is on the Willmore energy, i.e. the total squared mean curvature Our purpose is to address the delicate task of approximating global minimizers of the energy under boundary constraints.\n  The main contribution of this work is to translate the nonlinear boundary value problem into an integer linear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0777","kind":"arxiv","version":1},"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":"1101.0777","created_at":"2026-05-18T04:32:02.122553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0777v1","created_at":"2026-05-18T04:32:02.122553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0777","created_at":"2026-05-18T04:32:02.122553+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFQRW5KXERGA","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFQRW5KXERGAG24W","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFQRW5KX","created_at":"2026-05-18T12:26:24.575870+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/AFQRW5KXERGAG24WXGDVUNRAXT","json":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT.json","graph_json":"https://pith.science/api/pith-number/AFQRW5KXERGAG24WXGDVUNRAXT/graph.json","events_json":"https://pith.science/api/pith-number/AFQRW5KXERGAG24WXGDVUNRAXT/events.json","paper":"https://pith.science/paper/AFQRW5KX"},"agent_actions":{"view_html":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT","download_json":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT.json","view_paper":"https://pith.science/paper/AFQRW5KX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0777&json=true","fetch_graph":"https://pith.science/api/pith-number/AFQRW5KXERGAG24WXGDVUNRAXT/graph.json","fetch_events":"https://pith.science/api/pith-number/AFQRW5KXERGAG24WXGDVUNRAXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT/action/storage_attestation","attest_author":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT/action/author_attestation","sign_citation":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT/action/citation_signature","submit_replication":"https://pith.science/pith/AFQRW5KXERGAG24WXGDVUNRAXT/action/replication_record"}},"created_at":"2026-05-18T04:32:02.122553+00:00","updated_at":"2026-05-18T04:32:02.122553+00:00"}