{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KSLWRHOZZDLS5MSGLAS2NTKPKJ","short_pith_number":"pith:KSLWRHOZ","schema_version":"1.0","canonical_sha256":"5497689dd9c8d72eb2465825a6cd4f526a25606ec262aab1ddf298b999167096","source":{"kind":"arxiv","id":"1012.1289","version":1},"attestation_state":"computed","paper":{"title":"Classical Analysis and Nilpotent Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joseph A. Wolf","submitted_at":"2010-12-06T19:21:06Z","abstract_excerpt":"Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group structure. There are also some infinite dimensional analogs but I won't go into that here. The analytic ideas are not so different from those of the classical Fourier transform and Fourier inversion theories in one real variable."},"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":"1012.1289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-06T19:21:06Z","cross_cats_sorted":[],"title_canon_sha256":"1a48e77247c1b88828912c3537b0f6634eb0e80331dd0b49b8fc28b683512d27","abstract_canon_sha256":"4a5958ae580c0baced9f594c11123051bdfc524c225f2b31b71d6eaa4451f220"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:01.630684Z","signature_b64":"gPVbvZoFVuxU2SqSPFEyIwTjNAXyHxv+JIn6ggon80Rvwn8112CqNCZ9+TTnu3qDdGfN2sMjpMJQx5/1q3bgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5497689dd9c8d72eb2465825a6cd4f526a25606ec262aab1ddf298b999167096","last_reissued_at":"2026-05-18T04:34:01.630282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:01.630282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classical Analysis and Nilpotent Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joseph A. Wolf","submitted_at":"2010-12-06T19:21:06Z","abstract_excerpt":"Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group structure. There are also some infinite dimensional analogs but I won't go into that here. The analytic ideas are not so different from those of the classical Fourier transform and Fourier inversion theories in one real variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1289","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":"1012.1289","created_at":"2026-05-18T04:34:01.630341+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.1289v1","created_at":"2026-05-18T04:34:01.630341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1289","created_at":"2026-05-18T04:34:01.630341+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSLWRHOZZDLS","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSLWRHOZZDLS5MSG","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSLWRHOZ","created_at":"2026-05-18T12:26:09.077623+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/KSLWRHOZZDLS5MSGLAS2NTKPKJ","json":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ.json","graph_json":"https://pith.science/api/pith-number/KSLWRHOZZDLS5MSGLAS2NTKPKJ/graph.json","events_json":"https://pith.science/api/pith-number/KSLWRHOZZDLS5MSGLAS2NTKPKJ/events.json","paper":"https://pith.science/paper/KSLWRHOZ"},"agent_actions":{"view_html":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ","download_json":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ.json","view_paper":"https://pith.science/paper/KSLWRHOZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.1289&json=true","fetch_graph":"https://pith.science/api/pith-number/KSLWRHOZZDLS5MSGLAS2NTKPKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/KSLWRHOZZDLS5MSGLAS2NTKPKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ/action/storage_attestation","attest_author":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ/action/author_attestation","sign_citation":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ/action/citation_signature","submit_replication":"https://pith.science/pith/KSLWRHOZZDLS5MSGLAS2NTKPKJ/action/replication_record"}},"created_at":"2026-05-18T04:34:01.630341+00:00","updated_at":"2026-05-18T04:34:01.630341+00:00"}