{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BAO4HJSUZJ7X2DG3JGCRZ7M5YT","short_pith_number":"pith:BAO4HJSU","schema_version":"1.0","canonical_sha256":"081dc3a654ca7f7d0cdb49851cfd9dc4fe65d1c9cb0dbe81ec0d9ac1d0715706","source":{"kind":"arxiv","id":"1005.4794","version":1},"attestation_state":"computed","paper":{"title":"Consistency result for a non monotone scheme for anisotropic mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Antonin Chambolle, Elie Bretin, Eric Bonnetier","submitted_at":"2010-05-26T11:37:39Z","abstract_excerpt":"In this paper, we propose a new scheme for anisotropic motion by mean curvature in $\\R^d$. The scheme consists of a phase-field approximation of the motion, where the nonlinear diffusive terms in the corresponding anisotropic Allen-Cahn equation are linearized in the Fourier space. In real space, this corresponds to the convolution with a kernel of the form \\[ K_{\\phi,t}(x) = \\F^{-1}\\left[ e^{-4\\pi^2 t \\phi^o(\\xi)} \\right](x). \\] We analyse the resulting scheme, following the work of Ishii-Pires-Souganidis on the convergence of the Bence-Merriman-Osher algorithm for isotropic motion by mean cu"},"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":"1005.4794","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-05-26T11:37:39Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d8f1d052bba7783781504adad3cbe684dbea2b4802f99d8fbc83a1edb2d7ded4","abstract_canon_sha256":"516b3751db4dd2b9b76e3cb62857d874359d4fabf8e296ed18d97d7550f69b4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:37.623779Z","signature_b64":"WT5wwm9Bgh1nnCxbtwkD6yuKIMKmhoNMlYMSginSk4umiHccjsebZtuKJ17VpLFF+3ASXxet1e1c4oRlfmZ3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"081dc3a654ca7f7d0cdb49851cfd9dc4fe65d1c9cb0dbe81ec0d9ac1d0715706","last_reissued_at":"2026-06-03T23:06:37.623257Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:37.623257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consistency result for a non monotone scheme for anisotropic mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Antonin Chambolle, Elie Bretin, Eric Bonnetier","submitted_at":"2010-05-26T11:37:39Z","abstract_excerpt":"In this paper, we propose a new scheme for anisotropic motion by mean curvature in $\\R^d$. The scheme consists of a phase-field approximation of the motion, where the nonlinear diffusive terms in the corresponding anisotropic Allen-Cahn equation are linearized in the Fourier space. In real space, this corresponds to the convolution with a kernel of the form \\[ K_{\\phi,t}(x) = \\F^{-1}\\left[ e^{-4\\pi^2 t \\phi^o(\\xi)} \\right](x). \\] We analyse the resulting scheme, following the work of Ishii-Pires-Souganidis on the convergence of the Bence-Merriman-Osher algorithm for isotropic motion by mean cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4794","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1005.4794/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1005.4794","created_at":"2026-06-03T23:06:37.623345+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.4794v1","created_at":"2026-06-03T23:06:37.623345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4794","created_at":"2026-06-03T23:06:37.623345+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAO4HJSUZJ7X","created_at":"2026-06-03T23:06:37.623345+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAO4HJSUZJ7X2DG3","created_at":"2026-06-03T23:06:37.623345+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAO4HJSU","created_at":"2026-06-03T23:06:37.623345+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/BAO4HJSUZJ7X2DG3JGCRZ7M5YT","json":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT.json","graph_json":"https://pith.science/api/pith-number/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/graph.json","events_json":"https://pith.science/api/pith-number/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/events.json","paper":"https://pith.science/paper/BAO4HJSU"},"agent_actions":{"view_html":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT","download_json":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT.json","view_paper":"https://pith.science/paper/BAO4HJSU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.4794&json=true","fetch_graph":"https://pith.science/api/pith-number/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/graph.json","fetch_events":"https://pith.science/api/pith-number/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/action/storage_attestation","attest_author":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/action/author_attestation","sign_citation":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/action/citation_signature","submit_replication":"https://pith.science/pith/BAO4HJSUZJ7X2DG3JGCRZ7M5YT/action/replication_record"}},"created_at":"2026-06-03T23:06:37.623345+00:00","updated_at":"2026-06-03T23:06:37.623345+00:00"}