{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:BGPVM5EIULVXCAX2MVBX2XAWCB","short_pith_number":"pith:BGPVM5EI","schema_version":"1.0","canonical_sha256":"099f567488a2eb7102fa65437d5c16104974c320ce76cb31c68ac1b1954dfd9c","source":{"kind":"arxiv","id":"2405.20796","version":1},"attestation_state":"computed","paper":{"title":"Regularity of minimal surfaces with capillary boundary conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Carlo Gasparetto, Chao Li, Luigi De Masi, Nick Edelen","submitted_at":"2024-05-31T13:57:57Z","abstract_excerpt":"We prove $\\varepsilon$-regularity theorems for varifolds with capillary boundary condition in a Riemannian manifold. These varifolds were first introduced by Kagaya-Tonegawa \\cite{KaTo}. We establish a uniform first variation control for all such varifolds (and free-boundary varifolds generally) satisfying a sharp density bound and prove that if a capillary varifold has bounded mean curvature and is close to a capillary half-plane with angle not equal to $\\tfrac{\\pi}{2}$, then it coincides with a $C^{1,\\alpha}$ properly embedded hypersurface. We apply our theorem to deduce regularity at a gene"},"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":"2405.20796","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-31T13:57:57Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"82cbb85cef4ba51e35cfc4d64a8332ae917207c3ec3f76c86221283369d02bf1","abstract_canon_sha256":"55ff627ff90c98bc3ebda51a8eceb1b722202e00c62d26b910ba38e1a789778c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:42.154447Z","signature_b64":"VGXgddcONVlpfPiQ7jGmW7cNZ2k8zj6TY0tPy5pY2rXYjAvGYOgEKC0azSbvwFgRSU8U7oF+pk77zTn0zOuTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"099f567488a2eb7102fa65437d5c16104974c320ce76cb31c68ac1b1954dfd9c","last_reissued_at":"2026-07-05T08:25:42.154037Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:42.154037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of minimal surfaces with capillary boundary conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Carlo Gasparetto, Chao Li, Luigi De Masi, Nick Edelen","submitted_at":"2024-05-31T13:57:57Z","abstract_excerpt":"We prove $\\varepsilon$-regularity theorems for varifolds with capillary boundary condition in a Riemannian manifold. These varifolds were first introduced by Kagaya-Tonegawa \\cite{KaTo}. We establish a uniform first variation control for all such varifolds (and free-boundary varifolds generally) satisfying a sharp density bound and prove that if a capillary varifold has bounded mean curvature and is close to a capillary half-plane with angle not equal to $\\tfrac{\\pi}{2}$, then it coincides with a $C^{1,\\alpha}$ properly embedded hypersurface. We apply our theorem to deduce regularity at a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20796","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/2405.20796/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":"2405.20796","created_at":"2026-07-05T08:25:42.154103+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.20796v1","created_at":"2026-07-05T08:25:42.154103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.20796","created_at":"2026-07-05T08:25:42.154103+00:00"},{"alias_kind":"pith_short_12","alias_value":"BGPVM5EIULVX","created_at":"2026-07-05T08:25:42.154103+00:00"},{"alias_kind":"pith_short_16","alias_value":"BGPVM5EIULVXCAX2","created_at":"2026-07-05T08:25:42.154103+00:00"},{"alias_kind":"pith_short_8","alias_value":"BGPVM5EI","created_at":"2026-07-05T08:25:42.154103+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.02146","citing_title":"Weiss monotonicity and capillary hypersurfaces","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB","json":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB.json","graph_json":"https://pith.science/api/pith-number/BGPVM5EIULVXCAX2MVBX2XAWCB/graph.json","events_json":"https://pith.science/api/pith-number/BGPVM5EIULVXCAX2MVBX2XAWCB/events.json","paper":"https://pith.science/paper/BGPVM5EI"},"agent_actions":{"view_html":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB","download_json":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB.json","view_paper":"https://pith.science/paper/BGPVM5EI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.20796&json=true","fetch_graph":"https://pith.science/api/pith-number/BGPVM5EIULVXCAX2MVBX2XAWCB/graph.json","fetch_events":"https://pith.science/api/pith-number/BGPVM5EIULVXCAX2MVBX2XAWCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB/action/storage_attestation","attest_author":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB/action/author_attestation","sign_citation":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB/action/citation_signature","submit_replication":"https://pith.science/pith/BGPVM5EIULVXCAX2MVBX2XAWCB/action/replication_record"}},"created_at":"2026-07-05T08:25:42.154103+00:00","updated_at":"2026-07-05T08:25:42.154103+00:00"}