{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GS34SMNLJQF6EXXS57NXAG26WV","short_pith_number":"pith:GS34SMNL","schema_version":"1.0","canonical_sha256":"34b7c931ab4c0be25ef2efdb701b5eb55bab76970c82f12c45e1afd417f166fe","source":{"kind":"arxiv","id":"1703.09367","version":2},"attestation_state":"computed","paper":{"title":"Minimal hypersurfaces in the ball with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Glen Wheeler, Valentina-Mira Wheeler","submitted_at":"2017-03-28T01:50:38Z","abstract_excerpt":"In this note we use the strong maximum principle and integral estimates prove two results on minimal hypersurfaces $F:M^n\\rightarrow\\mathbb{R}^{n+1}$ with free boundary on the standard unit sphere. First we show that if $F$ is graphical with respect to any Killing field, then $F(M^n)$ is a flat disk. This result is independent of the topology or number or boundaries. Second, if $M^n = \\mathbb{D}^n$ is a disk, we show the supremum of the curvature squared on the interior is bounded below by $n$ times the infimum of the curvature squared on the boundary. These may be combined the give an impress"},"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":"1703.09367","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-28T01:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"ae5bcce791e11cf86fb88ccb2395b8070c77cb836ff857e2d9323b065286ca61","abstract_canon_sha256":"ad60dc9396e42a73ec453623d3e9aeeff33cb40749f3fe2815bdda23c7131052"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:18.820835Z","signature_b64":"dFYl3Woj5veXvjoNyC4SjoNuAgkpMALft7WVcTARbzCD2O8Pw2o4mzx2c2a4D6dcT0mfZF+Tkmg7O5Ze9XIPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b7c931ab4c0be25ef2efdb701b5eb55bab76970c82f12c45e1afd417f166fe","last_reissued_at":"2026-05-18T00:29:18.820170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:18.820170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal hypersurfaces in the ball with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Glen Wheeler, Valentina-Mira Wheeler","submitted_at":"2017-03-28T01:50:38Z","abstract_excerpt":"In this note we use the strong maximum principle and integral estimates prove two results on minimal hypersurfaces $F:M^n\\rightarrow\\mathbb{R}^{n+1}$ with free boundary on the standard unit sphere. First we show that if $F$ is graphical with respect to any Killing field, then $F(M^n)$ is a flat disk. This result is independent of the topology or number or boundaries. Second, if $M^n = \\mathbb{D}^n$ is a disk, we show the supremum of the curvature squared on the interior is bounded below by $n$ times the infimum of the curvature squared on the boundary. These may be combined the give an impress"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09367","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":"1703.09367","created_at":"2026-05-18T00:29:18.820270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.09367v2","created_at":"2026-05-18T00:29:18.820270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09367","created_at":"2026-05-18T00:29:18.820270+00:00"},{"alias_kind":"pith_short_12","alias_value":"GS34SMNLJQF6","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GS34SMNLJQF6EXXS","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GS34SMNL","created_at":"2026-05-18T12:31:18.294218+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/GS34SMNLJQF6EXXS57NXAG26WV","json":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV.json","graph_json":"https://pith.science/api/pith-number/GS34SMNLJQF6EXXS57NXAG26WV/graph.json","events_json":"https://pith.science/api/pith-number/GS34SMNLJQF6EXXS57NXAG26WV/events.json","paper":"https://pith.science/paper/GS34SMNL"},"agent_actions":{"view_html":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV","download_json":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV.json","view_paper":"https://pith.science/paper/GS34SMNL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.09367&json=true","fetch_graph":"https://pith.science/api/pith-number/GS34SMNLJQF6EXXS57NXAG26WV/graph.json","fetch_events":"https://pith.science/api/pith-number/GS34SMNLJQF6EXXS57NXAG26WV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV/action/storage_attestation","attest_author":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV/action/author_attestation","sign_citation":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV/action/citation_signature","submit_replication":"https://pith.science/pith/GS34SMNLJQF6EXXS57NXAG26WV/action/replication_record"}},"created_at":"2026-05-18T00:29:18.820270+00:00","updated_at":"2026-05-18T00:29:18.820270+00:00"}