{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WDIPZTBOO3CGV3CWJ2CXGUXZOB","short_pith_number":"pith:WDIPZTBO","schema_version":"1.0","canonical_sha256":"b0d0fccc2e76c46aec564e857352f970795e5c34c1294095a6c5794385cf23be","source":{"kind":"arxiv","id":"1204.1127","version":1},"attestation_state":"computed","paper":{"title":"Characterization of almost $L^p$-eigenfunctions of the Laplace-Beltrami operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pratyoosh Kumar, Rudra P. Sarkar, Swagato K. Ray","submitted_at":"2012-04-05T06:07:42Z","abstract_excerpt":"In \\cite{Roe} Roe proved that if a doubly-infinite sequence $\\{f_k\\}$ of functions on $\\R$ satisfies $f_{k+1}=(df_{k}/dx)$ and $|f_{k}(x)|\\leq M$ for all $k=0,\\pm 1,\\pm 2,...$ and $x\\in \\R$, then $f_0(x)=a\\sin(x+\\varphi)$ where $a$ and $\\varphi$ are real constants. This result was extended to $\\R^n$ by Strichartz \\cite{Str} where $d/dx$ is substituted by the Laplacian on $\\R^n$. While it is plausible to extend this theorem for other Riemannian manifolds or Lie groups, Strichartz showed that the result holds true for Heisenberg groups, but fails for hyperbolic 3-space. This negative result can "},"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":"1204.1127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-05T06:07:42Z","cross_cats_sorted":[],"title_canon_sha256":"86425ad884bfeffdaf349bd22235d56e250d6b57f89b05d8bd6f3496d02dfa40","abstract_canon_sha256":"c96301db205f02b3a871a394686920171b9cba33de43607b6a0d1f00ef393ce4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:36.315963Z","signature_b64":"Pjrnw84mcksvlZCFyExdJwxdcIL+w2QxqKxRDe4SSQVK9+5Ob0kJpWxJjPRaulxnOxOioDftYEbVflfiVMZEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0d0fccc2e76c46aec564e857352f970795e5c34c1294095a6c5794385cf23be","last_reissued_at":"2026-05-18T03:58:36.315402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:36.315402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of almost $L^p$-eigenfunctions of the Laplace-Beltrami operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pratyoosh Kumar, Rudra P. Sarkar, Swagato K. Ray","submitted_at":"2012-04-05T06:07:42Z","abstract_excerpt":"In \\cite{Roe} Roe proved that if a doubly-infinite sequence $\\{f_k\\}$ of functions on $\\R$ satisfies $f_{k+1}=(df_{k}/dx)$ and $|f_{k}(x)|\\leq M$ for all $k=0,\\pm 1,\\pm 2,...$ and $x\\in \\R$, then $f_0(x)=a\\sin(x+\\varphi)$ where $a$ and $\\varphi$ are real constants. This result was extended to $\\R^n$ by Strichartz \\cite{Str} where $d/dx$ is substituted by the Laplacian on $\\R^n$. While it is plausible to extend this theorem for other Riemannian manifolds or Lie groups, Strichartz showed that the result holds true for Heisenberg groups, but fails for hyperbolic 3-space. This negative result can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1127","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":""},"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":"1204.1127","created_at":"2026-05-18T03:58:36.315494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1127v1","created_at":"2026-05-18T03:58:36.315494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1127","created_at":"2026-05-18T03:58:36.315494+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDIPZTBOO3CG","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDIPZTBOO3CGV3CW","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDIPZTBO","created_at":"2026-05-18T12:27:25.539911+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/WDIPZTBOO3CGV3CWJ2CXGUXZOB","json":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB.json","graph_json":"https://pith.science/api/pith-number/WDIPZTBOO3CGV3CWJ2CXGUXZOB/graph.json","events_json":"https://pith.science/api/pith-number/WDIPZTBOO3CGV3CWJ2CXGUXZOB/events.json","paper":"https://pith.science/paper/WDIPZTBO"},"agent_actions":{"view_html":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB","download_json":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB.json","view_paper":"https://pith.science/paper/WDIPZTBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1127&json=true","fetch_graph":"https://pith.science/api/pith-number/WDIPZTBOO3CGV3CWJ2CXGUXZOB/graph.json","fetch_events":"https://pith.science/api/pith-number/WDIPZTBOO3CGV3CWJ2CXGUXZOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB/action/storage_attestation","attest_author":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB/action/author_attestation","sign_citation":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB/action/citation_signature","submit_replication":"https://pith.science/pith/WDIPZTBOO3CGV3CWJ2CXGUXZOB/action/replication_record"}},"created_at":"2026-05-18T03:58:36.315494+00:00","updated_at":"2026-05-18T03:58:36.315494+00:00"}