{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NAJPRVS2AXROEZZIJ4H7SWIZPB","short_pith_number":"pith:NAJPRVS2","schema_version":"1.0","canonical_sha256":"6812f8d65a05e2e267284f0ff9591978444bc3e8cf552430bbdb83b020fdbb93","source":{"kind":"arxiv","id":"2607.03930","version":1},"attestation_state":"computed","paper":{"title":"De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andrea Poiatti, Tim Laux","submitted_at":"2026-07-04T15:49:46Z","abstract_excerpt":"We propose an alternative existence proof of global weak solutions to mean curvature flow and volume preserving mean curvature flow. We prove for the first time for a minimizing movements scheme the unconditional convergence towards a varifold solution, here a De Giorgi solution. The argument is purely variational and does not rely on comparison principles. The key novelty is an alternative proxy for the completely degenerate $L^2$ distance that is more robust than the one of Almgren-Taylor-Wang and Luckhaus-Sturzenhecker."},"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":"2607.03930","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-04T15:49:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"2239fbc6d812e852bb1c411641fedb7d903747fcc66aa5298a831e63cfeab795","abstract_canon_sha256":"8e40e364857021573b075e2c4ce2086000ccfc90285a06ae1f7f02ee96ab0f81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:15.145092Z","signature_b64":"xO+/2qxI7WOEJXZkZ+5I9LxHA7cHlgk40//V9dX0baSM22VJ7xWtSYG5O5w7varNnErxUUIALJ2dY0VIpQ8gAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6812f8d65a05e2e267284f0ff9591978444bc3e8cf552430bbdb83b020fdbb93","last_reissued_at":"2026-07-07T02:18:15.144404Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:15.144404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andrea Poiatti, Tim Laux","submitted_at":"2026-07-04T15:49:46Z","abstract_excerpt":"We propose an alternative existence proof of global weak solutions to mean curvature flow and volume preserving mean curvature flow. We prove for the first time for a minimizing movements scheme the unconditional convergence towards a varifold solution, here a De Giorgi solution. The argument is purely variational and does not rely on comparison principles. The key novelty is an alternative proxy for the completely degenerate $L^2$ distance that is more robust than the one of Almgren-Taylor-Wang and Luckhaus-Sturzenhecker."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03930","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/2607.03930/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":"2607.03930","created_at":"2026-07-07T02:18:15.144531+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.03930v1","created_at":"2026-07-07T02:18:15.144531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03930","created_at":"2026-07-07T02:18:15.144531+00:00"},{"alias_kind":"pith_short_12","alias_value":"NAJPRVS2AXRO","created_at":"2026-07-07T02:18:15.144531+00:00"},{"alias_kind":"pith_short_16","alias_value":"NAJPRVS2AXROEZZI","created_at":"2026-07-07T02:18:15.144531+00:00"},{"alias_kind":"pith_short_8","alias_value":"NAJPRVS2","created_at":"2026-07-07T02:18:15.144531+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/NAJPRVS2AXROEZZIJ4H7SWIZPB","json":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB.json","graph_json":"https://pith.science/api/pith-number/NAJPRVS2AXROEZZIJ4H7SWIZPB/graph.json","events_json":"https://pith.science/api/pith-number/NAJPRVS2AXROEZZIJ4H7SWIZPB/events.json","paper":"https://pith.science/paper/NAJPRVS2"},"agent_actions":{"view_html":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB","download_json":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB.json","view_paper":"https://pith.science/paper/NAJPRVS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.03930&json=true","fetch_graph":"https://pith.science/api/pith-number/NAJPRVS2AXROEZZIJ4H7SWIZPB/graph.json","fetch_events":"https://pith.science/api/pith-number/NAJPRVS2AXROEZZIJ4H7SWIZPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB/action/storage_attestation","attest_author":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB/action/author_attestation","sign_citation":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB/action/citation_signature","submit_replication":"https://pith.science/pith/NAJPRVS2AXROEZZIJ4H7SWIZPB/action/replication_record"}},"created_at":"2026-07-07T02:18:15.144531+00:00","updated_at":"2026-07-07T02:18:15.144531+00:00"}