{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3AKGYJ6O4DLV5N7EIUXHYTIC6L","short_pith_number":"pith:3AKGYJ6O","schema_version":"1.0","canonical_sha256":"d8146c27cee0d75eb7e4452e7c4d02f2e75f9c304088687227e66b19fed6ac8c","source":{"kind":"arxiv","id":"2605.20371","version":1},"attestation_state":"computed","paper":{"title":"Arbitrary-order structure-preserving discretizations for geometric curvature flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Boris D. Andrews, Ganghui Zhang, Patrick E. Farrell","submitted_at":"2026-05-19T18:22:14Z","abstract_excerpt":"Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surface area while conserving volume; it is desirable to preserve these properties on discretization. This has motivated a substantial body of research on structure-preserving discretizations for these flows, albeit at low order in time. In this work, we present the first discretization of geometric curvature flows (curve shortening/mean curvature flow and curve/surface diffusion) that preserves the evolution of area and v"},"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":"2605.20371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-19T18:22:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a90f2144022fd007cd642ef1a18a8ca47261994c42fc204eb76143a4d98725bb","abstract_canon_sha256":"7643fecc97b870a9471a1360f160b808914546e1d3cc60830b62c296752ea0f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:35.387085Z","signature_b64":"5dmgQHPJSTahjhn1qQ98c+ZAMMO6DkjeCLaD/ATmbfcANFOkCF3CirdGpZhjum3wuK1JyH59Q2Qm5iM75wWoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8146c27cee0d75eb7e4452e7c4d02f2e75f9c304088687227e66b19fed6ac8c","last_reissued_at":"2026-05-21T01:04:35.386378Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:35.386378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arbitrary-order structure-preserving discretizations for geometric curvature flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Boris D. Andrews, Ganghui Zhang, Patrick E. Farrell","submitted_at":"2026-05-19T18:22:14Z","abstract_excerpt":"Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surface area while conserving volume; it is desirable to preserve these properties on discretization. This has motivated a substantial body of research on structure-preserving discretizations for these flows, albeit at low order in time. In this work, we present the first discretization of geometric curvature flows (curve shortening/mean curvature flow and curve/surface diffusion) that preserves the evolution of area and v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20371","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/2605.20371/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":"2605.20371","created_at":"2026-05-21T01:04:35.386484+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20371v1","created_at":"2026-05-21T01:04:35.386484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20371","created_at":"2026-05-21T01:04:35.386484+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AKGYJ6O4DLV","created_at":"2026-05-21T01:04:35.386484+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AKGYJ6O4DLV5N7E","created_at":"2026-05-21T01:04:35.386484+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AKGYJ6O","created_at":"2026-05-21T01:04:35.386484+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/3AKGYJ6O4DLV5N7EIUXHYTIC6L","json":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L.json","graph_json":"https://pith.science/api/pith-number/3AKGYJ6O4DLV5N7EIUXHYTIC6L/graph.json","events_json":"https://pith.science/api/pith-number/3AKGYJ6O4DLV5N7EIUXHYTIC6L/events.json","paper":"https://pith.science/paper/3AKGYJ6O"},"agent_actions":{"view_html":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L","download_json":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L.json","view_paper":"https://pith.science/paper/3AKGYJ6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20371&json=true","fetch_graph":"https://pith.science/api/pith-number/3AKGYJ6O4DLV5N7EIUXHYTIC6L/graph.json","fetch_events":"https://pith.science/api/pith-number/3AKGYJ6O4DLV5N7EIUXHYTIC6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L/action/storage_attestation","attest_author":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L/action/author_attestation","sign_citation":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L/action/citation_signature","submit_replication":"https://pith.science/pith/3AKGYJ6O4DLV5N7EIUXHYTIC6L/action/replication_record"}},"created_at":"2026-05-21T01:04:35.386484+00:00","updated_at":"2026-05-21T01:04:35.386484+00:00"}