{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2A5ATLPTXKNVI6VMCETYRE5QT","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":"4dadfdbd403af5329c4153c64691f3401a6d89cb14733b21bb90231e989bf6f9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-16T18:51:09Z","title_canon_sha256":"4e1f4ee06dc26a1d6f4bc517ca16c926332bb6687552a8d12397d69e7842536a"},"schema_version":"1.0","source":{"id":"1410.4533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4533","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4533v2","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4533","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"W2A5ATLPTXKN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2A5ATLPTXKNVI6V","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2A5ATLP","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:68d0ce85f2ba30862cd1f756cd6f47632a989f3469576d6b83855a8707d780c8","target":"graph","created_at":"2026-05-18T00:44:28Z","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 compute explicitly Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of various $p$-adic analytic and adelic profinite groups of type $\\mathsf{A}_2$. This has consequences for the representation zeta functions of arithmetic groups $\\Gamma \\subset \\mathbf{H}(k)$, where $k$ is a number field and $\\mathbf{H}$ a $k$-form of $\\mathsf{SL}_3$: assuming that $\\Gamma$ possesses the strong Congruence Subgroup Property, we obtain precise, uniform estimates for the representation growth of $\\Gamma$. Our results are based on explicit, uniform formulae for ","authors_text":"Benjamin Klopsch, Christopher Voll, Nir Avni, Uri Onn","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-16T18:51:09Z","title":"Similarity classes of integral $p$-adic matrices and representation zeta functions of groups of type $A_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4533","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:bc0bb5c3fcd6daca48130202fe64b80b83cceffd64d98d4780093fa08672cfac","target":"record","created_at":"2026-05-18T00:44:28Z","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":"4dadfdbd403af5329c4153c64691f3401a6d89cb14733b21bb90231e989bf6f9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-16T18:51:09Z","title_canon_sha256":"4e1f4ee06dc26a1d6f4bc517ca16c926332bb6687552a8d12397d69e7842536a"},"schema_version":"1.0","source":{"id":"1410.4533","kind":"arxiv","version":2}},"canonical_sha256":"b681d04d6f9dd4daa3d560893c449d84fbecaf19e493d5f6e1f005c6e998ed1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b681d04d6f9dd4daa3d560893c449d84fbecaf19e493d5f6e1f005c6e998ed1d","first_computed_at":"2026-05-18T00:44:28.744746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.744746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gzqx3zFWxbxY7eMb+lwcMWEYIe4Ep29sJtfSI9RMLoecbYPdCamxlBrrX1QFlZk4h3F94qmxK3tG3O9T9sZjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.745241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0bb5c3fcd6daca48130202fe64b80b83cceffd64d98d4780093fa08672cfac","sha256:68d0ce85f2ba30862cd1f756cd6f47632a989f3469576d6b83855a8707d780c8"],"state_sha256":"f21661dab1eed5474ae8a9480fb98402ed22af3ab7795c5df943eec8b967cd38"}