{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QXKQFE3I455TCLLVM44FHTD7M4","short_pith_number":"pith:QXKQFE3I","schema_version":"1.0","canonical_sha256":"85d5029368e77b312d75673853cc7f671485b43aa98f642d745e0e61393e8de0","source":{"kind":"arxiv","id":"1110.6092","version":4},"attestation_state":"computed","paper":{"title":"Arithmetic groups, base change, and representation growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Christopher Voll, Nir Avni, Uri Onn","submitted_at":"2011-10-27T14:38:30Z","abstract_excerpt":"Consider an arithmetic group $\\mathbf{G}(O_S)$, where $\\mathbf{G}$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of $S$-integers $O_S$ of a number field $K$ with respect to a finite set of places $S$. For each $n \\in \\mathbb{N}$, let $R_n(\\mathbf{G}(O_S))$ denote the number of irreducible complex representations of $\\mathbf{G}(O_S)$ of dimension at most $n$. The degree of representation growth $\\alpha(\\mathbf{G}(O_S)) = \\lim_{n \\rightarrow \\infty} \\log R_n(\\mathbf{G}(O_S)) / \\log n$ is finite if and only if $\\mathbf{G}("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1110.6092","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-27T14:38:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a0c71fcf77a88a6ba0a0a58b7738cb34d431da944e2f2d94cef5c3adeb6e04b2","abstract_canon_sha256":"07b83a45c71af499b3ec47a1b4d555d30d5e55c9eb89b12f004d352ba45623b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:09.007520Z","signature_b64":"ZY3yBPvsxT+xqm6F2zyEUSzypSraCEGe0P8mfdyMGAyo89l5Uqr4VXIz91SlsCdAUGxgVqbDR2BZuQadvw01CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85d5029368e77b312d75673853cc7f671485b43aa98f642d745e0e61393e8de0","last_reissued_at":"2026-05-18T01:22:09.006898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:09.006898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic groups, base change, and representation growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Christopher Voll, Nir Avni, Uri Onn","submitted_at":"2011-10-27T14:38:30Z","abstract_excerpt":"Consider an arithmetic group $\\mathbf{G}(O_S)$, where $\\mathbf{G}$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of $S$-integers $O_S$ of a number field $K$ with respect to a finite set of places $S$. For each $n \\in \\mathbb{N}$, let $R_n(\\mathbf{G}(O_S))$ denote the number of irreducible complex representations of $\\mathbf{G}(O_S)$ of dimension at most $n$. The degree of representation growth $\\alpha(\\mathbf{G}(O_S)) = \\lim_{n \\rightarrow \\infty} \\log R_n(\\mathbf{G}(O_S)) / \\log n$ is finite if and only if $\\mathbf{G}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6092","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1110.6092","created_at":"2026-05-18T01:22:09.006980+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6092v4","created_at":"2026-05-18T01:22:09.006980+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6092","created_at":"2026-05-18T01:22:09.006980+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXKQFE3I455T","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXKQFE3I455TCLLV","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXKQFE3I","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4","json":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4.json","graph_json":"https://pith.science/api/pith-number/QXKQFE3I455TCLLVM44FHTD7M4/graph.json","events_json":"https://pith.science/api/pith-number/QXKQFE3I455TCLLVM44FHTD7M4/events.json","paper":"https://pith.science/paper/QXKQFE3I"},"agent_actions":{"view_html":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4","download_json":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4.json","view_paper":"https://pith.science/paper/QXKQFE3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6092&json=true","fetch_graph":"https://pith.science/api/pith-number/QXKQFE3I455TCLLVM44FHTD7M4/graph.json","fetch_events":"https://pith.science/api/pith-number/QXKQFE3I455TCLLVM44FHTD7M4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4/action/storage_attestation","attest_author":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4/action/author_attestation","sign_citation":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4/action/citation_signature","submit_replication":"https://pith.science/pith/QXKQFE3I455TCLLVM44FHTD7M4/action/replication_record"}},"created_at":"2026-05-18T01:22:09.006980+00:00","updated_at":"2026-05-18T01:22:09.006980+00:00"}