{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VX7MGWOQDRPBFXVEQXD4BY22KX","short_pith_number":"pith:VX7MGWOQ","schema_version":"1.0","canonical_sha256":"adfec359d01c5e12dea485c7c0e35a55f2b6b219c3726ec4fd5b0d33845475c1","source":{"kind":"arxiv","id":"2507.13148","version":1},"attestation_state":"computed","paper":{"title":"On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Neshan Wickramasekera, Paul Minter, Spencer Becker-Kahn","submitted_at":"2025-07-17T14:13:29Z","abstract_excerpt":"We study stationary integral $n$-varifolds $V$ in the unit ball $B_1(0)\\subset\\mathbb{R}^{n+k}$. Allard's regularity theorem establishes the existence of $\\epsilon = \\epsilon(n,k)\\in (0,1)$ for which if $V$ is $\\epsilon$-close (as varifolds) to the plane $P_0 = \\{0\\}^k\\times\\mathbb{R}^n$ with multiplicity 1 then, in $B_{1/2}(0)$, $V$ is represented by a single $C^{1,\\alpha}$ minimal graph. However, when instead $P_0$ occurs with multiplicity $Q\\in \\{2,3,\\dotsc\\}$, simple examples show that this conclusion, now as a multi-valued graph, may fail, even if $V$ corresponds to an area-minimising rec"},"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":"2507.13148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-17T14:13:29Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e9c704b93c640a7826236e8798b9cd9319a517a4bfaf6d0049e421cdc681b33c","abstract_canon_sha256":"b5814763711122aed8f87dc5353411f2397395b45af2b5193fc62abbdbc278cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:55.440562Z","signature_b64":"O9WM0/Yp7IQTUnfoi5K6lIEk8t8hofnV1Pg8n3n5/IHFZ19QdN1kWTZllPakszyl3bTSb3C00nBv+o2qriAdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adfec359d01c5e12dea485c7c0e35a55f2b6b219c3726ec4fd5b0d33845475c1","last_reissued_at":"2026-07-05T11:38:55.440030Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:55.440030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Neshan Wickramasekera, Paul Minter, Spencer Becker-Kahn","submitted_at":"2025-07-17T14:13:29Z","abstract_excerpt":"We study stationary integral $n$-varifolds $V$ in the unit ball $B_1(0)\\subset\\mathbb{R}^{n+k}$. Allard's regularity theorem establishes the existence of $\\epsilon = \\epsilon(n,k)\\in (0,1)$ for which if $V$ is $\\epsilon$-close (as varifolds) to the plane $P_0 = \\{0\\}^k\\times\\mathbb{R}^n$ with multiplicity 1 then, in $B_{1/2}(0)$, $V$ is represented by a single $C^{1,\\alpha}$ minimal graph. However, when instead $P_0$ occurs with multiplicity $Q\\in \\{2,3,\\dotsc\\}$, simple examples show that this conclusion, now as a multi-valued graph, may fail, even if $V$ corresponds to an area-minimising rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13148","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/2507.13148/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":"2507.13148","created_at":"2026-07-05T11:38:55.440081+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.13148v1","created_at":"2026-07-05T11:38:55.440081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13148","created_at":"2026-07-05T11:38:55.440081+00:00"},{"alias_kind":"pith_short_12","alias_value":"VX7MGWOQDRPB","created_at":"2026-07-05T11:38:55.440081+00:00"},{"alias_kind":"pith_short_16","alias_value":"VX7MGWOQDRPBFXVE","created_at":"2026-07-05T11:38:55.440081+00:00"},{"alias_kind":"pith_short_8","alias_value":"VX7MGWOQ","created_at":"2026-07-05T11:38:55.440081+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01511","citing_title":"A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05041","citing_title":"An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX","json":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX.json","graph_json":"https://pith.science/api/pith-number/VX7MGWOQDRPBFXVEQXD4BY22KX/graph.json","events_json":"https://pith.science/api/pith-number/VX7MGWOQDRPBFXVEQXD4BY22KX/events.json","paper":"https://pith.science/paper/VX7MGWOQ"},"agent_actions":{"view_html":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX","download_json":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX.json","view_paper":"https://pith.science/paper/VX7MGWOQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.13148&json=true","fetch_graph":"https://pith.science/api/pith-number/VX7MGWOQDRPBFXVEQXD4BY22KX/graph.json","fetch_events":"https://pith.science/api/pith-number/VX7MGWOQDRPBFXVEQXD4BY22KX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX/action/storage_attestation","attest_author":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX/action/author_attestation","sign_citation":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX/action/citation_signature","submit_replication":"https://pith.science/pith/VX7MGWOQDRPBFXVEQXD4BY22KX/action/replication_record"}},"created_at":"2026-07-05T11:38:55.440081+00:00","updated_at":"2026-07-05T11:38:55.440081+00:00"}