{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BE3ZXBZNF4D62O57TLGRUPCAUJ","short_pith_number":"pith:BE3ZXBZN","schema_version":"1.0","canonical_sha256":"09379b872d2f07ed3bbf9acd1a3c40a25f61b6352b1aefa5dfb1ba02173092b5","source":{"kind":"arxiv","id":"1405.1903","version":2},"attestation_state":"computed","paper":{"title":"Convergence of nodal sets in the adiabatic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Jonas Lampart","submitted_at":"2014-05-08T12:29:48Z","abstract_excerpt":"We study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles $\\pi{:}\\, M\\to B$ in the adiabatic limit. This limit consists in considering a family $G_\\varepsilon$ of Riemannian metrics, that are close to Riemannian submersions, for which the ratio of the diameter of the fibres to that of the base is given by $\\varepsilon \\ll 1$.\n  We assume $M$ to be compact and allow for fibres $F$ with boundary, under the condition that the ground state eigenvalue of the Dirichlet-Laplacian on $F_x$ is independent of the base point. We prove for $\\mathrm{dim} B \\leq 3$ that the "},"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":"1405.1903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-08T12:29:48Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"29fde8088267532752abd198fff7ae81a43de19a1cd4ff2a31e195026a8ab337","abstract_canon_sha256":"8cf4bad17026c63b6f0f5fea2aeb2ea5d9f9c5941171355f2f06c8673d8b17e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:09.948517Z","signature_b64":"wsCuwSZDFZRMujNVQcb+Hx/a2nIJPRe5FFkWp2w6Jfo/jGixLLKicsnmYz256gByFoUYNXZybr1UZnbTJ5EHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09379b872d2f07ed3bbf9acd1a3c40a25f61b6352b1aefa5dfb1ba02173092b5","last_reissued_at":"2026-05-18T02:38:09.947840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:09.947840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of nodal sets in the adiabatic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Jonas Lampart","submitted_at":"2014-05-08T12:29:48Z","abstract_excerpt":"We study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles $\\pi{:}\\, M\\to B$ in the adiabatic limit. This limit consists in considering a family $G_\\varepsilon$ of Riemannian metrics, that are close to Riemannian submersions, for which the ratio of the diameter of the fibres to that of the base is given by $\\varepsilon \\ll 1$.\n  We assume $M$ to be compact and allow for fibres $F$ with boundary, under the condition that the ground state eigenvalue of the Dirichlet-Laplacian on $F_x$ is independent of the base point. We prove for $\\mathrm{dim} B \\leq 3$ that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1903","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":"1405.1903","created_at":"2026-05-18T02:38:09.947948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.1903v2","created_at":"2026-05-18T02:38:09.947948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1903","created_at":"2026-05-18T02:38:09.947948+00:00"},{"alias_kind":"pith_short_12","alias_value":"BE3ZXBZNF4D6","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BE3ZXBZNF4D62O57","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BE3ZXBZN","created_at":"2026-05-18T12:28:22.404517+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/BE3ZXBZNF4D62O57TLGRUPCAUJ","json":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ.json","graph_json":"https://pith.science/api/pith-number/BE3ZXBZNF4D62O57TLGRUPCAUJ/graph.json","events_json":"https://pith.science/api/pith-number/BE3ZXBZNF4D62O57TLGRUPCAUJ/events.json","paper":"https://pith.science/paper/BE3ZXBZN"},"agent_actions":{"view_html":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ","download_json":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ.json","view_paper":"https://pith.science/paper/BE3ZXBZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.1903&json=true","fetch_graph":"https://pith.science/api/pith-number/BE3ZXBZNF4D62O57TLGRUPCAUJ/graph.json","fetch_events":"https://pith.science/api/pith-number/BE3ZXBZNF4D62O57TLGRUPCAUJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ/action/storage_attestation","attest_author":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ/action/author_attestation","sign_citation":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ/action/citation_signature","submit_replication":"https://pith.science/pith/BE3ZXBZNF4D62O57TLGRUPCAUJ/action/replication_record"}},"created_at":"2026-05-18T02:38:09.947948+00:00","updated_at":"2026-05-18T02:38:09.947948+00:00"}