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Our second result is the Bernstein type one \\emph{there is no entire graphs of $\\mathbb{R}^4$ with zero scalar curvature such that $\\dfrac{(-K)}{H^3}\\geq c>0$ everywhere}. At last, it will be proved that, if there exists a stable hypersurface with zero scalar curvature and $\\dfra"},"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":"1305.5819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-24T18:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"94adc0767932d7ee49c91f4c257d4e7052307294483ae6bf207bef36e49a5c2b","abstract_canon_sha256":"5f7e0cc0072f4e0b0b031a405de985988f54175dc13383f0ae28d977d6d4bb8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.342493Z","signature_b64":"iYQ1ci5fmDI5f8RbRo3oyq/CECZaRSEyQ6Lfj7pUPDLzgCOlnMxVZCNB8RC8r/r0F50ZhtvDilN7kKXXg1d6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fafbe3c6e51583deab263571bf53488f432392cb0480c68ab3244003d7d6041","last_reissued_at":"2026-05-18T00:46:32.342046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.342046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Stable Hypersurfaces with Vanishing Scalar Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Greg\\'orio Silva Neto","submitted_at":"2013-05-24T18:26:31Z","abstract_excerpt":"We will prove that \\emph{there are no stable complete hypersurfaces of $\\mathbb{R}^4$ with zero scalar curvature, polynomial volume growth and such that $\\dfrac{(-K)}{H^3}\\geq c>0$ everywhere, for some constant $c>0$}, where $K$ denotes the Gauss-Kronecker curvature and $H$ denotes the mean curvature of the immersion. Our second result is the Bernstein type one \\emph{there is no entire graphs of $\\mathbb{R}^4$ with zero scalar curvature such that $\\dfrac{(-K)}{H^3}\\geq c>0$ everywhere}. At last, it will be proved that, if there exists a stable hypersurface with zero scalar curvature and $\\dfra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5819","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":"1305.5819","created_at":"2026-05-18T00:46:32.342111+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5819v2","created_at":"2026-05-18T00:46:32.342111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5819","created_at":"2026-05-18T00:46:32.342111+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6X34PDOKFMD","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6X34PDOKFMD32VS","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6X34PDO","created_at":"2026-05-18T12:27:59.945178+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/T6X34PDOKFMD32VSMNLRX5JURD","json":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD.json","graph_json":"https://pith.science/api/pith-number/T6X34PDOKFMD32VSMNLRX5JURD/graph.json","events_json":"https://pith.science/api/pith-number/T6X34PDOKFMD32VSMNLRX5JURD/events.json","paper":"https://pith.science/paper/T6X34PDO"},"agent_actions":{"view_html":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD","download_json":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD.json","view_paper":"https://pith.science/paper/T6X34PDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5819&json=true","fetch_graph":"https://pith.science/api/pith-number/T6X34PDOKFMD32VSMNLRX5JURD/graph.json","fetch_events":"https://pith.science/api/pith-number/T6X34PDOKFMD32VSMNLRX5JURD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD/action/storage_attestation","attest_author":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD/action/author_attestation","sign_citation":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD/action/citation_signature","submit_replication":"https://pith.science/pith/T6X34PDOKFMD32VSMNLRX5JURD/action/replication_record"}},"created_at":"2026-05-18T00:46:32.342111+00:00","updated_at":"2026-05-18T00:46:32.342111+00:00"}