{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BYCP42ZMJYKL4QIT6Y552HZ6ZS","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":"32bacd0f1817c3fa5c4afebcacfc53092f378a8fa9d52b78eecb6f881a11d63a","cross_cats_sorted":["math.GR","math.SP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-11-10T11:47:08Z","title_canon_sha256":"ebe84e9c12a1eeaea0ce00c124921de91793e44e6dec5f9017868ddfddcf2eff"},"schema_version":"1.0","source":{"id":"2511.06996","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.06996","created_at":"2026-08-04T02:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"2511.06996v2","created_at":"2026-08-04T02:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.06996","created_at":"2026-08-04T02:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"BYCP42ZMJYKL","created_at":"2026-08-04T02:09:05Z"},{"alias_kind":"pith_short_16","alias_value":"BYCP42ZMJYKL4QIT","created_at":"2026-08-04T02:09:05Z"},{"alias_kind":"pith_short_8","alias_value":"BYCP42ZM","created_at":"2026-08-04T02:09:05Z"}],"graph_snapshots":[{"event_id":"sha256:72347452635df9e1698b3fa619d1fe2fbdc333b6618050663a6ae53793d54381","target":"graph","created_at":"2026-08-04T02:09:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.06996/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a real semisimple Lie group $G$ with finite center and a discrete subgroup $\\Gamma \\subset G$ whose limit cone is disjoint from two facets of the Weyl chamber we show that Quint's growth indicator function $\\psi_\\Gamma$ is bounded by the half sum of positive roots $\\rho$, i.e. it has slow growth, implying that the representation $L^2(\\Gamma \\backslash G)$ is tempered. In particular, this holds for each $I$-Anosov subgroup provided that $I$ contains at least two distinct simple roots that are not interchanged by the opposition involution.","authors_text":"Lasse Lennart Wolf","cross_cats":["math.GR","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-11-10T11:47:08Z","title":"The limit cone and bounds on the growth indicator function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.06996","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:fd23aa67867416f390529dc28ff6b30110155ab9fc79a79177e07d29b0259088","target":"record","created_at":"2026-08-04T02:09:05Z","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":"32bacd0f1817c3fa5c4afebcacfc53092f378a8fa9d52b78eecb6f881a11d63a","cross_cats_sorted":["math.GR","math.SP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-11-10T11:47:08Z","title_canon_sha256":"ebe84e9c12a1eeaea0ce00c124921de91793e44e6dec5f9017868ddfddcf2eff"},"schema_version":"1.0","source":{"id":"2511.06996","kind":"arxiv","version":2}},"canonical_sha256":"0e04fe6b2c4e14be4113f63bdd1f3ecc9880d1f306ca0140b9c4c43773efe3b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e04fe6b2c4e14be4113f63bdd1f3ecc9880d1f306ca0140b9c4c43773efe3b0","first_computed_at":"2026-08-04T02:09:05.367088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:09:05.367088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qmA/GUrwuzKb1iqSqB94mxVI2gsPfc31fKtcmzhSucKV64YxWYzuQ2dzjbcGSsF2KZojS2vZTRNSqVvyxgglDQ==","signature_status":"signed_v1","signed_at":"2026-08-04T02:09:05.368965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.06996","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd23aa67867416f390529dc28ff6b30110155ab9fc79a79177e07d29b0259088","sha256:72347452635df9e1698b3fa619d1fe2fbdc333b6618050663a6ae53793d54381"],"state_sha256":"c361f4bba65d035279c134d44adc9c9cd642a78841f03915bd0f9b963cdb9b71"}