{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XTDGQFTFFAFQGBXSPRHWNOVIQY","short_pith_number":"pith:XTDGQFTF","schema_version":"1.0","canonical_sha256":"bcc6681665280b0306f27c4f66baa8860bb2c20fef7eddec5c5dc8124bd109e4","source":{"kind":"arxiv","id":"1212.2540","version":2},"attestation_state":"computed","paper":{"title":"Improvement of eigenfunction estimates on manifolds of nonpositive curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Melissa Tacy","submitted_at":"2012-12-11T17:06:30Z","abstract_excerpt":"Let $(M,g)$ be a compact, boundaryless manifold of dimension $n$ with the property that either (i) $n=2$ and $(M,g)$ has no conjugate points, or (ii) the sectional curvatures of $(M,g)$ are nonpositive. Let $\\Delta$ be the positive Laplacian on $M$ determined by $g$. We study the $L^{2}\\to{}L^{p}$ mapping properties of a spectral cluster of $\\sqrt{\\Delta}$ of width $1/\\log\\lambda$. Under the geometric assumptions above, \\cite{berard77} B\\'{e}rard obtained a logarithmic improvement for the remainder term of the eigenvalue counting function which directly leads to a $(\\log\\lambda)^{1/2}$ improve"},"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":"1212.2540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-11T17:06:30Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"84a6fd321eb4398f37a55fccc6aef50e9b889233205ca28a356c6fcb8f75113e","abstract_canon_sha256":"e3ae228f5d351f07aedd0c71e5842717fee82bd07186009d5b650e9dbf92cd55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:49.177369Z","signature_b64":"rZkKaKoev2scMEFaPyepMOk8/3aCXtu2g2jCoewdlJxD43FZ601in0Vca4Dkxh/C4QWp5NLGZCJGB9y49//BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcc6681665280b0306f27c4f66baa8860bb2c20fef7eddec5c5dc8124bd109e4","last_reissued_at":"2026-05-18T01:22:49.176799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:49.176799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improvement of eigenfunction estimates on manifolds of nonpositive curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Melissa Tacy","submitted_at":"2012-12-11T17:06:30Z","abstract_excerpt":"Let $(M,g)$ be a compact, boundaryless manifold of dimension $n$ with the property that either (i) $n=2$ and $(M,g)$ has no conjugate points, or (ii) the sectional curvatures of $(M,g)$ are nonpositive. Let $\\Delta$ be the positive Laplacian on $M$ determined by $g$. We study the $L^{2}\\to{}L^{p}$ mapping properties of a spectral cluster of $\\sqrt{\\Delta}$ of width $1/\\log\\lambda$. Under the geometric assumptions above, \\cite{berard77} B\\'{e}rard obtained a logarithmic improvement for the remainder term of the eigenvalue counting function which directly leads to a $(\\log\\lambda)^{1/2}$ improve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2540","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":"1212.2540","created_at":"2026-05-18T01:22:49.176876+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2540v2","created_at":"2026-05-18T01:22:49.176876+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2540","created_at":"2026-05-18T01:22:49.176876+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTDGQFTFFAFQ","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTDGQFTFFAFQGBXS","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTDGQFTF","created_at":"2026-05-18T12:27:27.928770+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/XTDGQFTFFAFQGBXSPRHWNOVIQY","json":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY.json","graph_json":"https://pith.science/api/pith-number/XTDGQFTFFAFQGBXSPRHWNOVIQY/graph.json","events_json":"https://pith.science/api/pith-number/XTDGQFTFFAFQGBXSPRHWNOVIQY/events.json","paper":"https://pith.science/paper/XTDGQFTF"},"agent_actions":{"view_html":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY","download_json":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY.json","view_paper":"https://pith.science/paper/XTDGQFTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2540&json=true","fetch_graph":"https://pith.science/api/pith-number/XTDGQFTFFAFQGBXSPRHWNOVIQY/graph.json","fetch_events":"https://pith.science/api/pith-number/XTDGQFTFFAFQGBXSPRHWNOVIQY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY/action/storage_attestation","attest_author":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY/action/author_attestation","sign_citation":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY/action/citation_signature","submit_replication":"https://pith.science/pith/XTDGQFTFFAFQGBXSPRHWNOVIQY/action/replication_record"}},"created_at":"2026-05-18T01:22:49.176876+00:00","updated_at":"2026-05-18T01:22:49.176876+00:00"}