{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:5HK6XXBAAJCCNXRAX4KPYFAMJE","short_pith_number":"pith:5HK6XXBA","schema_version":"1.0","canonical_sha256":"e9d5ebdc20024426de20bf14fc140c492a809e07e6ec10be10b9ca38c4050040","source":{"kind":"arxiv","id":"2212.11939","version":1},"attestation_state":"computed","paper":{"title":"Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Clemens Ullrich, Kerrek Stinson, Tim Laux","submitted_at":"2022-12-22T18:20:34Z","abstract_excerpt":"The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models, and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak-strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals."},"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":"2212.11939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T18:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"7e45992d7ed3914167bcdeacaf5fb584954c4bfc308f80813b0850fd87a2b8b2","abstract_canon_sha256":"0c04ead9f30a2ee83df9dd2dd135d7804c753639c05ff7e59a8946ad71267d7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:27:44.893377Z","signature_b64":"gdv6U6+ICPcQb0RQZ0ZJsmK+9totHTUqJNW/fR9w4+Tm5tIZ6F3ffqAGkYgdaUU/cQIae6k0aNvkP0aC0Hd8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9d5ebdc20024426de20bf14fc140c492a809e07e6ec10be10b9ca38c4050040","last_reissued_at":"2026-07-05T05:27:44.892941Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:27:44.892941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Clemens Ullrich, Kerrek Stinson, Tim Laux","submitted_at":"2022-12-22T18:20:34Z","abstract_excerpt":"The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models, and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak-strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11939","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/2212.11939/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":"2212.11939","created_at":"2026-07-05T05:27:44.893005+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.11939v1","created_at":"2026-07-05T05:27:44.893005+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11939","created_at":"2026-07-05T05:27:44.893005+00:00"},{"alias_kind":"pith_short_12","alias_value":"5HK6XXBAAJCC","created_at":"2026-07-05T05:27:44.893005+00:00"},{"alias_kind":"pith_short_16","alias_value":"5HK6XXBAAJCCNXRA","created_at":"2026-07-05T05:27:44.893005+00:00"},{"alias_kind":"pith_short_8","alias_value":"5HK6XXBA","created_at":"2026-07-05T05:27:44.893005+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/5HK6XXBAAJCCNXRAX4KPYFAMJE","json":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE.json","graph_json":"https://pith.science/api/pith-number/5HK6XXBAAJCCNXRAX4KPYFAMJE/graph.json","events_json":"https://pith.science/api/pith-number/5HK6XXBAAJCCNXRAX4KPYFAMJE/events.json","paper":"https://pith.science/paper/5HK6XXBA"},"agent_actions":{"view_html":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE","download_json":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE.json","view_paper":"https://pith.science/paper/5HK6XXBA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.11939&json=true","fetch_graph":"https://pith.science/api/pith-number/5HK6XXBAAJCCNXRAX4KPYFAMJE/graph.json","fetch_events":"https://pith.science/api/pith-number/5HK6XXBAAJCCNXRAX4KPYFAMJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE/action/storage_attestation","attest_author":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE/action/author_attestation","sign_citation":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE/action/citation_signature","submit_replication":"https://pith.science/pith/5HK6XXBAAJCCNXRAX4KPYFAMJE/action/replication_record"}},"created_at":"2026-07-05T05:27:44.893005+00:00","updated_at":"2026-07-05T05:27:44.893005+00:00"}