{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G2ORNZKLVA6B52QBMV427SIKP6","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":"5da5c39ca5ab053c09b7e60e83a92b89479d714ea59bdc9f1f41327e154ed4fc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T14:33:07Z","title_canon_sha256":"895317be7d6fb9832ad49ebca14173dd9de444fd4b54562d1c4d71ef4593aae3"},"schema_version":"1.0","source":{"id":"1610.06429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06429","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06429v2","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06429","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"G2ORNZKLVA6B","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2ORNZKLVA6B52QB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2ORNZKL","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:db472370c50b1949e93aa3cfccf82c3155f995b6aac1dddad426b242b6e9c112","target":"graph","created_at":"2026-05-18T00:57:39Z","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 prove a generalization of Schur orthogonality relations for certain classes of representations of Gromov hyperbolic groups. We apply the obtained results to show that representations of non-abelian free groups associated to the Patterson-Sullivan measures corresponding to a wide class of invariant metrics on the group are monotonous in the sense introduced by Kuhn and Steger. This in particular includes representations associated to harmonic measures of a wide class of random walks.","authors_text":"Adrien Boyer, {\\L}ukasz Garncarek","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T14:33:07Z","title":"Asymptotic Schur orthogonality in hyperbolic groups with application to monotony"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06429","kind":"arxiv","version":2},"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:b55327f195bd0eeda2b89f3634bc8acac70d9ef35737f3752ae734708ce6be08","target":"record","created_at":"2026-05-18T00:57:39Z","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":"5da5c39ca5ab053c09b7e60e83a92b89479d714ea59bdc9f1f41327e154ed4fc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T14:33:07Z","title_canon_sha256":"895317be7d6fb9832ad49ebca14173dd9de444fd4b54562d1c4d71ef4593aae3"},"schema_version":"1.0","source":{"id":"1610.06429","kind":"arxiv","version":2}},"canonical_sha256":"369d16e54ba83c1eea016579afc90a7fbaadc06ca6377d065f5eccdd2dc54623","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"369d16e54ba83c1eea016579afc90a7fbaadc06ca6377d065f5eccdd2dc54623","first_computed_at":"2026-05-18T00:57:39.330625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:39.330625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtmNn3yimeSR4I11H1PEP6+5AfyJE+3HT7Y8XWYT2jT7V97ILP0FPxeskq/T7Teo6JK/QdqAA7f+th+ogC10Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:39.331284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b55327f195bd0eeda2b89f3634bc8acac70d9ef35737f3752ae734708ce6be08","sha256:db472370c50b1949e93aa3cfccf82c3155f995b6aac1dddad426b242b6e9c112"],"state_sha256":"0035008f92df071a5b138d3da513ad1e63886f5f91ce08d08acbe662d8228ce8"}