{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UZZOZMMM43AYUPCG46BTGW7YFI","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":"0a2bb23cf7becda6c410692e436d32f86241f771decd4bc61763d68b70525b6d","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-01T14:06:33Z","title_canon_sha256":"23663718a0f1dfcb6336e0a073221b6a4afa51fc58319a0479d4218c1f26c587"},"schema_version":"1.0","source":{"id":"1307.0371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0371","created_at":"2026-05-18T02:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0371v2","created_at":"2026-05-18T02:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0371","created_at":"2026-05-18T02:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"UZZOZMMM43AY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UZZOZMMM43AYUPCG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UZZOZMMM","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:8fe1dcb4866cad56218f11cb046368a7ace317bcc64ac0c74a5b7e96cfa922c6","target":"graph","created_at":"2026-05-18T02:57:52Z","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 relate the asymptotic representation theory of $SL(d,\\mathbb{Z}_p)$ and the singularities of the moduli space of $SL(d)$-local systems on a smooth projective curve, proving new theorems about both. Regarding the former, we prove that, for every d, the number of n-dimensional representations of $SL(d,\\mathbb{Z}_p)$ grows slower than $n^{22}$, confirming a conjecture of Larsen and Lubotzky. Regarding the latter, we prove that the moduli space of $SL(d)$-local systems on a smooth projective curve of genus at least 12 has rational singularities. Most of our results apply more generally to semi-","authors_text":"Avraham Aizenbud, Nir Avni","cross_cats":["math.GR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-01T14:06:33Z","title":"Representation Growth and Rational Singularities of the Moduli Space of Local Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0371","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:aebb74e59fd997daf6ed9d67bb18cdbf67cb979dd11c3bf9dfe92614a961ff5e","target":"record","created_at":"2026-05-18T02:57:52Z","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":"0a2bb23cf7becda6c410692e436d32f86241f771decd4bc61763d68b70525b6d","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-01T14:06:33Z","title_canon_sha256":"23663718a0f1dfcb6336e0a073221b6a4afa51fc58319a0479d4218c1f26c587"},"schema_version":"1.0","source":{"id":"1307.0371","kind":"arxiv","version":2}},"canonical_sha256":"a672ecb18ce6c18a3c46e783335bf82a13f1903f7ed9fc6b5668c65d379cdcef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a672ecb18ce6c18a3c46e783335bf82a13f1903f7ed9fc6b5668c65d379cdcef","first_computed_at":"2026-05-18T02:57:52.838231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:52.838231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oyrBEon3UfpLyfpTx6EMIDVI2LNm+u3+loLB8jCdwjX69t2SOEcFw/QLNoQsXzscDaA9YWH7DZBUPo9J2kO6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:52.838758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aebb74e59fd997daf6ed9d67bb18cdbf67cb979dd11c3bf9dfe92614a961ff5e","sha256:8fe1dcb4866cad56218f11cb046368a7ace317bcc64ac0c74a5b7e96cfa922c6"],"state_sha256":"11b009a32fb6eac1b93c35148b7c3272b69592488d2b2da72a458f83cbfe2cca"}