{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YP26JYAESX5DBZ7WT5VOGFGPQU","short_pith_number":"pith:YP26JYAE","schema_version":"1.0","canonical_sha256":"c3f5e4e00495fa30e7f69f6ae314cf85061e67645a542fde45d385943fdc3b2f","source":{"kind":"arxiv","id":"1112.3565","version":2},"attestation_state":"computed","paper":{"title":"Global regularity for minimal sets near a $\\T$ set and counterexamples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xiangyu Liang","submitted_at":"2011-12-15T16:48:54Z","abstract_excerpt":"We discuss the global regularity for 2 dimensional minimal sets that are near a $\\T$ set, that is, whether every global minimal set in $\\R^n$ that looks like a $\\T$ set at infinity is a $\\T$ set or not. The main point is to use the topological properties of a minimal set at large scale to control its topology at smaller scales. This is the idea to prove that all 1-dimensional Almgren-minimal sets in $\\R^n$, and all 2-dimensional Mumford-Shah minimal sets in $\\R^3$ are cones. In this article we discuss two types of 2-dimensional minimal sets: Almgren-minimal set in $\\R^3$ whose blow-in limit is"},"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":"1112.3565","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-15T16:48:54Z","cross_cats_sorted":[],"title_canon_sha256":"2be602a24dab11eebbe31ca80be216515e7ad2a5e5766826dcccb387e1db3182","abstract_canon_sha256":"a0bf5835298de2501173384ae526cdc3bb43561d2b3883221bba0dc5a87b1271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:01.563003Z","signature_b64":"CWr6/JgR4r7CDZvJffpThxNvkdsM/fYQ7Hrig88ZDJMyEi0OCKArY0FZgA8X8Fv3r4xap2ZxZS4vLG8wiAL0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3f5e4e00495fa30e7f69f6ae314cf85061e67645a542fde45d385943fdc3b2f","last_reissued_at":"2026-05-18T04:01:01.562235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:01.562235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global regularity for minimal sets near a $\\T$ set and counterexamples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xiangyu Liang","submitted_at":"2011-12-15T16:48:54Z","abstract_excerpt":"We discuss the global regularity for 2 dimensional minimal sets that are near a $\\T$ set, that is, whether every global minimal set in $\\R^n$ that looks like a $\\T$ set at infinity is a $\\T$ set or not. The main point is to use the topological properties of a minimal set at large scale to control its topology at smaller scales. This is the idea to prove that all 1-dimensional Almgren-minimal sets in $\\R^n$, and all 2-dimensional Mumford-Shah minimal sets in $\\R^3$ are cones. In this article we discuss two types of 2-dimensional minimal sets: Almgren-minimal set in $\\R^3$ whose blow-in limit is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3565","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":""},"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":"1112.3565","created_at":"2026-05-18T04:01:01.562372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3565v2","created_at":"2026-05-18T04:01:01.562372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3565","created_at":"2026-05-18T04:01:01.562372+00:00"},{"alias_kind":"pith_short_12","alias_value":"YP26JYAESX5D","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YP26JYAESX5DBZ7W","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YP26JYAE","created_at":"2026-05-18T12:26:47.523578+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/YP26JYAESX5DBZ7WT5VOGFGPQU","json":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU.json","graph_json":"https://pith.science/api/pith-number/YP26JYAESX5DBZ7WT5VOGFGPQU/graph.json","events_json":"https://pith.science/api/pith-number/YP26JYAESX5DBZ7WT5VOGFGPQU/events.json","paper":"https://pith.science/paper/YP26JYAE"},"agent_actions":{"view_html":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU","download_json":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU.json","view_paper":"https://pith.science/paper/YP26JYAE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3565&json=true","fetch_graph":"https://pith.science/api/pith-number/YP26JYAESX5DBZ7WT5VOGFGPQU/graph.json","fetch_events":"https://pith.science/api/pith-number/YP26JYAESX5DBZ7WT5VOGFGPQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU/action/storage_attestation","attest_author":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU/action/author_attestation","sign_citation":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU/action/citation_signature","submit_replication":"https://pith.science/pith/YP26JYAESX5DBZ7WT5VOGFGPQU/action/replication_record"}},"created_at":"2026-05-18T04:01:01.562372+00:00","updated_at":"2026-05-18T04:01:01.562372+00:00"}