{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N7SA57ZYAOZES65LMPOB6D6MJX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"88a463af98972bcbabb1538da5c16e6a1891c416200e55bf2f704ab9605f5eb3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-21T13:45:15Z","title_canon_sha256":"539c1f717170fa4eee896a2cb6bbbdb9778f6d32912238a22caeba01b13a0a1e"},"schema_version":"1.0","source":{"id":"1311.5400","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5400","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5400v3","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5400","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"N7SA57ZYAOZE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N7SA57ZYAOZES65L","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N7SA57ZY","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:aeb0d286b90bf6bb08e83e3c7d02488cd30fbcefad09db75192a9e2c4f8160b1","target":"graph","created_at":"2026-05-18T00:50:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for this to be the case.\n  As an application, we show that when P is the minimal parabolic subgroup in one of the classical simple Lie groups of real rank one or the exceptional such group, then the Fourier algebra of P coincides with the subalgebra of the Fourier-Stieltjes algebra of P consisting of functions vanishing at infinity. In particular, the regular rep","authors_text":"S{\\o}ren Knudby","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-21T13:45:15Z","title":"Fourier algebras of parabolic subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5400","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b3e3ca655e6c42c0d4be0ba27df7bd0ffb6c8a2133f3c606e3cb3458488bf288","target":"record","created_at":"2026-05-18T00:50:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"88a463af98972bcbabb1538da5c16e6a1891c416200e55bf2f704ab9605f5eb3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-21T13:45:15Z","title_canon_sha256":"539c1f717170fa4eee896a2cb6bbbdb9778f6d32912238a22caeba01b13a0a1e"},"schema_version":"1.0","source":{"id":"1311.5400","kind":"arxiv","version":3}},"canonical_sha256":"6fe40eff3803b2497bab63dc1f0fcc4dc1c811cab8910bfedcccd0c5bca930ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fe40eff3803b2497bab63dc1f0fcc4dc1c811cab8910bfedcccd0c5bca930ac","first_computed_at":"2026-05-18T00:50:02.353249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:02.353249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zSTnwC7DuzM3Xek9PMVWplEp47gUnY6RpWq2rdflCHjVgWRqu1tbXCsnlAP8xRxQvwPjnzYPsOLfzqWg3Hc0AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:02.354018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5400","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3e3ca655e6c42c0d4be0ba27df7bd0ffb6c8a2133f3c606e3cb3458488bf288","sha256:aeb0d286b90bf6bb08e83e3c7d02488cd30fbcefad09db75192a9e2c4f8160b1"],"state_sha256":"a9de752d8a6c503cec2214e4a7e0d8599ab7f5916ab2627db0352e017839e144"}