{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XAHDKAM7FEXRG7544TJZ5G2GEX","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":"9c9973d550651ce6eb0a1212839804e584e45a09db8ad0b2683bfe341c4788b2","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-08T08:54:14Z","title_canon_sha256":"2e5831779adf35283dc111fb73a361493dbb6170f68c7d3379ac155fd7a56dd1"},"schema_version":"1.0","source":{"id":"1409.2245","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2245","created_at":"2026-05-18T00:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2245v3","created_at":"2026-05-18T00:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2245","created_at":"2026-05-18T00:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"XAHDKAM7FEXR","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XAHDKAM7FEXRG754","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XAHDKAM7","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:851068d7fcb0cf158736156a4d64e90f93a52f904578587e4da949b67e672c47","target":"graph","created_at":"2026-05-18T00:00:13Z","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":"By employing a new strategy we prove that all parabolically induced unitary representations of the Burger-Mozes universal group U(F)^+, with F being primitive, have all their matrix coefficients vanishing at infinity. This generalizes the same well-known result for the universal group U(F)^+, when F is 2-transitive.","authors_text":"Corina Ciobotaru","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-08T08:54:14Z","title":"Parabolically induced unitary representations of the universal group U(F)^+ are C_0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2245","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:b6e53134dd320fb94909817e9a839349acdd224f45969281d8fe563f422d68aa","target":"record","created_at":"2026-05-18T00:00:13Z","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":"9c9973d550651ce6eb0a1212839804e584e45a09db8ad0b2683bfe341c4788b2","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-08T08:54:14Z","title_canon_sha256":"2e5831779adf35283dc111fb73a361493dbb6170f68c7d3379ac155fd7a56dd1"},"schema_version":"1.0","source":{"id":"1409.2245","kind":"arxiv","version":3}},"canonical_sha256":"b80e35019f292f137fbce4d39e9b4625f2c8c1584857c9645d863c77108fd3b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80e35019f292f137fbce4d39e9b4625f2c8c1584857c9645d863c77108fd3b7","first_computed_at":"2026-05-18T00:00:13.911554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:13.911554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p3E6V/qiVh0fVJYnXmHJXP6C0NtmCv5n1YHmuWTuOdBLClaOwXIvqAXYNNUQgQL4fup4HZb22PAveJT0hYY/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:13.912099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2245","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e53134dd320fb94909817e9a839349acdd224f45969281d8fe563f422d68aa","sha256:851068d7fcb0cf158736156a4d64e90f93a52f904578587e4da949b67e672c47"],"state_sha256":"d7a61c90ce4bcf1ba2231fa2c2a32bccc689b75f7121cbd475171e0109cf5420"}