{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UUD7TDJHWUTBC4TNIJNVRJTAGZ","short_pith_number":"pith:UUD7TDJH","schema_version":"1.0","canonical_sha256":"a507f98d27b52611726d425b58a66036495dc36af71d43eacec7001aa5f3ee77","source":{"kind":"arxiv","id":"2407.09193","version":2},"attestation_state":"computed","paper":{"title":"Classical solutions to the soap film capillarity problem for plane boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bozhidar Velichkov, Giulia Bevilacqua, Salvatore Stuvard","submitted_at":"2024-07-12T11:51:13Z","abstract_excerpt":"We study the soap film capillarity problem, in which soap films are modeled as sets of least perimeter among those having prescribed (small) volume and satisfying a topological spanning condition. When the given boundary is the closed tubular neighborhood in $\\mathbb{R}^3$ of a smooth Jordan curve (or, more generally, the closed tubular neighborhood in $\\mathbb{R}^d$ of a smooth embedding of $\\mathbb{S}^{d-2}$ in a hyperplane), we prove existence and uniqueness of classical minimizers, for which the collapsing phenomenon does not occur. We show that the boundary of the unique minimizer is the "},"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":"2407.09193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-12T11:51:13Z","cross_cats_sorted":[],"title_canon_sha256":"563419f0200ee199382f28abab20798a949fcc95290c7d636700c797ec176a87","abstract_canon_sha256":"18ebbc0eb22370eb4e3230771a263b4ad1e143f95f9fdf254c65cc363f1dbfc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:43.086481Z","signature_b64":"Dr/KuQB9aMQVIoYse6oV1qf+7wupe3qeMtqOfX/3K/Yu799Aru1D98ew5c0txbREMT3qKIAtCMO8uU1/ZQt9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a507f98d27b52611726d425b58a66036495dc36af71d43eacec7001aa5f3ee77","last_reissued_at":"2026-07-05T11:26:43.085991Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:43.085991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classical solutions to the soap film capillarity problem for plane boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bozhidar Velichkov, Giulia Bevilacqua, Salvatore Stuvard","submitted_at":"2024-07-12T11:51:13Z","abstract_excerpt":"We study the soap film capillarity problem, in which soap films are modeled as sets of least perimeter among those having prescribed (small) volume and satisfying a topological spanning condition. When the given boundary is the closed tubular neighborhood in $\\mathbb{R}^3$ of a smooth Jordan curve (or, more generally, the closed tubular neighborhood in $\\mathbb{R}^d$ of a smooth embedding of $\\mathbb{S}^{d-2}$ in a hyperplane), we prove existence and uniqueness of classical minimizers, for which the collapsing phenomenon does not occur. We show that the boundary of the unique minimizer is the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09193","kind":"arxiv","version":2},"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/2407.09193/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":"2407.09193","created_at":"2026-07-05T11:26:43.086047+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.09193v2","created_at":"2026-07-05T11:26:43.086047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.09193","created_at":"2026-07-05T11:26:43.086047+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUD7TDJHWUTB","created_at":"2026-07-05T11:26:43.086047+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUD7TDJHWUTBC4TN","created_at":"2026-07-05T11:26:43.086047+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUD7TDJH","created_at":"2026-07-05T11:26:43.086047+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/UUD7TDJHWUTBC4TNIJNVRJTAGZ","json":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ.json","graph_json":"https://pith.science/api/pith-number/UUD7TDJHWUTBC4TNIJNVRJTAGZ/graph.json","events_json":"https://pith.science/api/pith-number/UUD7TDJHWUTBC4TNIJNVRJTAGZ/events.json","paper":"https://pith.science/paper/UUD7TDJH"},"agent_actions":{"view_html":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ","download_json":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ.json","view_paper":"https://pith.science/paper/UUD7TDJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.09193&json=true","fetch_graph":"https://pith.science/api/pith-number/UUD7TDJHWUTBC4TNIJNVRJTAGZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UUD7TDJHWUTBC4TNIJNVRJTAGZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ/action/storage_attestation","attest_author":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ/action/author_attestation","sign_citation":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ/action/citation_signature","submit_replication":"https://pith.science/pith/UUD7TDJHWUTBC4TNIJNVRJTAGZ/action/replication_record"}},"created_at":"2026-07-05T11:26:43.086047+00:00","updated_at":"2026-07-05T11:26:43.086047+00:00"}