{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IOHPCUMQI2UVU54TOUOFKMOECF","short_pith_number":"pith:IOHPCUMQ","schema_version":"1.0","canonical_sha256":"438ef1519046a95a7793751c5531c4116b675a268e4eb7b6a739a9e10513bb0c","source":{"kind":"arxiv","id":"1605.02589","version":3},"attestation_state":"computed","paper":{"title":"Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Alexander Logunov","submitted_at":"2016-05-09T14:03:22Z","abstract_excerpt":"Let $u$ be a harmonic function in the unit ball $B(0,1) \\subset \\mathbb{R}^n$, $n \\geq 3$, such that $u(0)=0$. Nadirashvili conjectured that there exists a positive constant $c$, depending on the dimension $n$ only, such that $H^{n-1}(\\{u=0 \\}\\cap B) \\geq c$. We prove Nadirashvili's conjecture as well as its counterpart on $C^\\infty$-smooth Riemannian manifolds. The latter yields the lower bound in Yau's conjecture. Namely, we show that for any compact $C^\\infty$-smooth Riemannian manifold $M$ (without boundary) of dimension $n$ there exists $c>0$ such that for any Laplace eigenfunction $\\varp"},"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":"1605.02589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-09T14:03:22Z","cross_cats_sorted":["math.CA","math.DG","math.SP"],"title_canon_sha256":"f5e010da14b538ff8f8dd72a5fd23248dafd21bacbad9aac4306c8383ddf0f06","abstract_canon_sha256":"fa1f3e8cea4dad94a2208e5c13768531f572a0a77462497a639c91a9724418eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:10.312606Z","signature_b64":"LLdzzkMzs/c2Z5LJlXPXHD1WNERxiZ0W5TtPn0jmcrQULkys0gCYw110LyDB7A+fylwgEmBxrcdyzWkabPgEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"438ef1519046a95a7793751c5531c4116b675a268e4eb7b6a739a9e10513bb0c","last_reissued_at":"2026-05-17T23:45:10.311939Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:10.311939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Alexander Logunov","submitted_at":"2016-05-09T14:03:22Z","abstract_excerpt":"Let $u$ be a harmonic function in the unit ball $B(0,1) \\subset \\mathbb{R}^n$, $n \\geq 3$, such that $u(0)=0$. Nadirashvili conjectured that there exists a positive constant $c$, depending on the dimension $n$ only, such that $H^{n-1}(\\{u=0 \\}\\cap B) \\geq c$. We prove Nadirashvili's conjecture as well as its counterpart on $C^\\infty$-smooth Riemannian manifolds. The latter yields the lower bound in Yau's conjecture. Namely, we show that for any compact $C^\\infty$-smooth Riemannian manifold $M$ (without boundary) of dimension $n$ there exists $c>0$ such that for any Laplace eigenfunction $\\varp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02589","kind":"arxiv","version":3},"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":"1605.02589","created_at":"2026-05-17T23:45:10.312036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02589v3","created_at":"2026-05-17T23:45:10.312036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02589","created_at":"2026-05-17T23:45:10.312036+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOHPCUMQI2UV","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOHPCUMQI2UVU54T","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOHPCUMQ","created_at":"2026-05-18T12:30:22.444734+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/IOHPCUMQI2UVU54TOUOFKMOECF","json":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF.json","graph_json":"https://pith.science/api/pith-number/IOHPCUMQI2UVU54TOUOFKMOECF/graph.json","events_json":"https://pith.science/api/pith-number/IOHPCUMQI2UVU54TOUOFKMOECF/events.json","paper":"https://pith.science/paper/IOHPCUMQ"},"agent_actions":{"view_html":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF","download_json":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF.json","view_paper":"https://pith.science/paper/IOHPCUMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02589&json=true","fetch_graph":"https://pith.science/api/pith-number/IOHPCUMQI2UVU54TOUOFKMOECF/graph.json","fetch_events":"https://pith.science/api/pith-number/IOHPCUMQI2UVU54TOUOFKMOECF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF/action/storage_attestation","attest_author":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF/action/author_attestation","sign_citation":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF/action/citation_signature","submit_replication":"https://pith.science/pith/IOHPCUMQI2UVU54TOUOFKMOECF/action/replication_record"}},"created_at":"2026-05-17T23:45:10.312036+00:00","updated_at":"2026-05-17T23:45:10.312036+00:00"}