{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:HBEYROOPK4V7DWLFVRRJ55YZPI","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":"bc95276aceab3210a3b3e6ffeb64f363fa04ea2b4304d3e7685409a604893113","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2004-09-20T11:10:54Z","title_canon_sha256":"ec410eb573ad8f3b1231de224de352493627034b175be35d1dffd4be40e1bbb4"},"schema_version":"1.0","source":{"id":"math/0409345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409345","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409345v1","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409345","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"HBEYROOPK4V7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"HBEYROOPK4V7DWLF","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"HBEYROOP","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d3840568e7c4d1822c95c378c3a8327bafe31cf0e4097eada81c60de586c1905","target":"graph","created_at":"2026-05-18T03:32:18Z","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 that any non-cocompact irreducible lattice in a higher rank semi-simple Lie group contains a subgroup of finite index, which has three generators.","authors_text":"Ritumoni Sarma, T.N.Venkataramana","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2004-09-20T11:10:54Z","title":"Generators for Arithmetic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409345","kind":"arxiv","version":1},"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":"sha256:803462b1ebdc8f1da1fd26307b3f19d833d4584490a85a166765fef2e5edda37","target":"record","created_at":"2026-05-18T03:32:18Z","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":"bc95276aceab3210a3b3e6ffeb64f363fa04ea2b4304d3e7685409a604893113","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2004-09-20T11:10:54Z","title_canon_sha256":"ec410eb573ad8f3b1231de224de352493627034b175be35d1dffd4be40e1bbb4"},"schema_version":"1.0","source":{"id":"math/0409345","kind":"arxiv","version":1}},"canonical_sha256":"384988b9cf572bf1d965ac629ef7197a129469af173bdd39d4b1b967927c4ea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"384988b9cf572bf1d965ac629ef7197a129469af173bdd39d4b1b967927c4ea3","first_computed_at":"2026-05-18T03:32:18.000136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:18.000136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+GV4+M4HOPz7eaawhCit9incfu6NWXqFonzePbBukwP5gdlS9wSVu3313zkuWqJ+kpDMcEWao7tlgh01vTWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:18.000886Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0409345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:803462b1ebdc8f1da1fd26307b3f19d833d4584490a85a166765fef2e5edda37","sha256:d3840568e7c4d1822c95c378c3a8327bafe31cf0e4097eada81c60de586c1905"],"state_sha256":"7282e5b4c8664dd6eb8ebbe958b22bc9c7fcfadb6f89e605cbdf9dd7660f7d1e"}