{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:P4HU272UDN2O35CAA2RJ4CHQ4G","short_pith_number":"pith:P4HU272U","schema_version":"1.0","canonical_sha256":"7f0f4d7f541b74edf44006a29e08f0e1bfb58b7513738106c784171e1c1561a2","source":{"kind":"arxiv","id":"1110.0655","version":3},"attestation_state":"computed","paper":{"title":"Direct Systems of Spherical Functions and Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.RT","authors_text":"Gestur Olafsson, Joseph A. Wolf, Matthew Dawson","submitted_at":"2011-10-04T12:24:03Z","abstract_excerpt":"Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\\infty/K_\\infty = \\varinjlim G_n/K_n$. We use the representation theoretic construction $\\phi (x) = <e, \\pi(x)e>$ where $e$ is a $K_\\infty$--fixed unit vector for $\\pi$. Specifically, we look at representations $\\pi_\\infty = \\varinjlim \\pi_n$ of $G_\\infty$ where $\\pi_n$ is $K_n$--spherical, so the spherical representations $\\pi_n$ and the corre"},"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":"1110.0655","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-04T12:24:03Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"50fbc4fdaee167ae07752314348b85a7c53bba9e28c37b3f7c485ab208113d23","abstract_canon_sha256":"f809662a6a9f60a0bd227bc35d6e7815a4021cbca5d96a325b74e02d704cfca8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:12.684575Z","signature_b64":"3iPOnK0kUz7Ar2+oEXsTiVZxc07kwSkacy1Va/KJRUQsKF6wDCAXgah32WgPeiEVhQdCTgMnI+YsFXZz07+gBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f0f4d7f541b74edf44006a29e08f0e1bfb58b7513738106c784171e1c1561a2","last_reissued_at":"2026-05-18T03:41:12.684030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:12.684030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Direct Systems of Spherical Functions and Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.RT","authors_text":"Gestur Olafsson, Joseph A. Wolf, Matthew Dawson","submitted_at":"2011-10-04T12:24:03Z","abstract_excerpt":"Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\\infty/K_\\infty = \\varinjlim G_n/K_n$. We use the representation theoretic construction $\\phi (x) = <e, \\pi(x)e>$ where $e$ is a $K_\\infty$--fixed unit vector for $\\pi$. Specifically, we look at representations $\\pi_\\infty = \\varinjlim \\pi_n$ of $G_\\infty$ where $\\pi_n$ is $K_n$--spherical, so the spherical representations $\\pi_n$ and the corre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0655","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":"1110.0655","created_at":"2026-05-18T03:41:12.684114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0655v3","created_at":"2026-05-18T03:41:12.684114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0655","created_at":"2026-05-18T03:41:12.684114+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4HU272UDN2O","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4HU272UDN2O35CA","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4HU272U","created_at":"2026-05-18T12:26:39.201973+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/P4HU272UDN2O35CAA2RJ4CHQ4G","json":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G.json","graph_json":"https://pith.science/api/pith-number/P4HU272UDN2O35CAA2RJ4CHQ4G/graph.json","events_json":"https://pith.science/api/pith-number/P4HU272UDN2O35CAA2RJ4CHQ4G/events.json","paper":"https://pith.science/paper/P4HU272U"},"agent_actions":{"view_html":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G","download_json":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G.json","view_paper":"https://pith.science/paper/P4HU272U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0655&json=true","fetch_graph":"https://pith.science/api/pith-number/P4HU272UDN2O35CAA2RJ4CHQ4G/graph.json","fetch_events":"https://pith.science/api/pith-number/P4HU272UDN2O35CAA2RJ4CHQ4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G/action/storage_attestation","attest_author":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G/action/author_attestation","sign_citation":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G/action/citation_signature","submit_replication":"https://pith.science/pith/P4HU272UDN2O35CAA2RJ4CHQ4G/action/replication_record"}},"created_at":"2026-05-18T03:41:12.684114+00:00","updated_at":"2026-05-18T03:41:12.684114+00:00"}