{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PTFZB37KWCEOHC6MTHXIGBC7AV","short_pith_number":"pith:PTFZB37K","schema_version":"1.0","canonical_sha256":"7ccb90efeab088e38bcc99ee83045f0579c0b527e57e20125fa5c71491c7d0c6","source":{"kind":"arxiv","id":"2607.05755","version":1},"attestation_state":"computed","paper":{"title":"Topological Bernstein Theorems for Minimal Hypersurfaces in $\\R^4$ confined in space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander D. McWeeney, Shrey Aryan","submitted_at":"2026-07-07T02:26:45Z","abstract_excerpt":"The three-dimensional catenoid in $\\R^4$ is a complete embedded minimal hypersurface contained in a slab, showing that the half-space theorem does not extend directly to higher dimensions. We show that this obstruction is topological in $\\R^4$. Specifically, we show that a complete, properly embedded minimal hypersurface $\\Sigma^3\\subset\\R^4$ with bounded curvature, diffeomorphic to $\\R^3$, and contained in a slab must be a hyperplane. Under the additional assumption of cubic volume growth, the same conclusion holds for minimal hypersurfaces contained in a half-space."},"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":"2607.05755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-07T02:26:45Z","cross_cats_sorted":[],"title_canon_sha256":"f27999b4ebf61a57aaab1fe0df97a1fa168f2c66375f04eccc99253359e0a1dc","abstract_canon_sha256":"ff19a962444f633e8f0f3cb84101ef6305aaa3182050d37ddbf7a2d35561cef6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:43.958437Z","signature_b64":"JuTyzEJH43S1+lot38Oowh/mfaCxNoiAPsIUe/v/5zSzF3g4o7hBjxBUGsbdv+AzM/+U8XsXhe1ZjrBk+fw8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ccb90efeab088e38bcc99ee83045f0579c0b527e57e20125fa5c71491c7d0c6","last_reissued_at":"2026-07-08T01:18:43.958006Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:43.958006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Bernstein Theorems for Minimal Hypersurfaces in $\\R^4$ confined in space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander D. McWeeney, Shrey Aryan","submitted_at":"2026-07-07T02:26:45Z","abstract_excerpt":"The three-dimensional catenoid in $\\R^4$ is a complete embedded minimal hypersurface contained in a slab, showing that the half-space theorem does not extend directly to higher dimensions. We show that this obstruction is topological in $\\R^4$. Specifically, we show that a complete, properly embedded minimal hypersurface $\\Sigma^3\\subset\\R^4$ with bounded curvature, diffeomorphic to $\\R^3$, and contained in a slab must be a hyperplane. Under the additional assumption of cubic volume growth, the same conclusion holds for minimal hypersurfaces contained in a half-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05755","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/2607.05755/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":"2607.05755","created_at":"2026-07-08T01:18:43.958070+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.05755v1","created_at":"2026-07-08T01:18:43.958070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05755","created_at":"2026-07-08T01:18:43.958070+00:00"},{"alias_kind":"pith_short_12","alias_value":"PTFZB37KWCEO","created_at":"2026-07-08T01:18:43.958070+00:00"},{"alias_kind":"pith_short_16","alias_value":"PTFZB37KWCEOHC6M","created_at":"2026-07-08T01:18:43.958070+00:00"},{"alias_kind":"pith_short_8","alias_value":"PTFZB37K","created_at":"2026-07-08T01:18:43.958070+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04364","citing_title":"Calabi-Yau Conjecture for Minimal Hypersurfaces in $\\mathbb{R}^4$ with bounded geometry","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV","json":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV.json","graph_json":"https://pith.science/api/pith-number/PTFZB37KWCEOHC6MTHXIGBC7AV/graph.json","events_json":"https://pith.science/api/pith-number/PTFZB37KWCEOHC6MTHXIGBC7AV/events.json","paper":"https://pith.science/paper/PTFZB37K"},"agent_actions":{"view_html":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV","download_json":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV.json","view_paper":"https://pith.science/paper/PTFZB37K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.05755&json=true","fetch_graph":"https://pith.science/api/pith-number/PTFZB37KWCEOHC6MTHXIGBC7AV/graph.json","fetch_events":"https://pith.science/api/pith-number/PTFZB37KWCEOHC6MTHXIGBC7AV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV/action/storage_attestation","attest_author":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV/action/author_attestation","sign_citation":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV/action/citation_signature","submit_replication":"https://pith.science/pith/PTFZB37KWCEOHC6MTHXIGBC7AV/action/replication_record"}},"created_at":"2026-07-08T01:18:43.958070+00:00","updated_at":"2026-07-08T01:18:43.958070+00:00"}