{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LISFTORFJ4X5M3FGXSCRUH6VEC","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":"8105f6e7064ef4fabd6c6e4cb384d6d7ba9fdd0a583112786130d12006cff342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-11T17:24:35Z","title_canon_sha256":"19172632ee930f211a42cb276a926b5d8cfb29e77e840a3c6b44be5afa21f62b"},"schema_version":"1.0","source":{"id":"1801.03887","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03887","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03887v2","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03887","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"LISFTORFJ4X5","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LISFTORFJ4X5M3FG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LISFTORF","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:e71eacfed887230562a1ac583e426f7fae663a37ee47e7ade4512851491a2fb8","target":"graph","created_at":"2026-05-17T23:43:07Z","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 two results about width of words in $SL_n(\\mathbb{Z})$. The first is that, for every $n \\geq 3$, there is a constant $C(n)$ such that the width of any word in $SL_n(\\mathbb{Z})$ is less than $C(n)$. The second result is that, for any word $w$, if $n$ is big enough, the width of $w$ in $SL_n(\\mathbb{Z})$ is at most 87.","authors_text":"Chen Meiri, Nir Avni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-11T17:24:35Z","title":"Words have bounded width in $SL(n,\\mathbb{Z})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03887","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:ca41200e51aa6d29c3cb80c56966e3b20aea904c683318cc9f8015e126641748","target":"record","created_at":"2026-05-17T23:43:07Z","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":"8105f6e7064ef4fabd6c6e4cb384d6d7ba9fdd0a583112786130d12006cff342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-11T17:24:35Z","title_canon_sha256":"19172632ee930f211a42cb276a926b5d8cfb29e77e840a3c6b44be5afa21f62b"},"schema_version":"1.0","source":{"id":"1801.03887","kind":"arxiv","version":2}},"canonical_sha256":"5a2459ba254f2fd66ca6bc851a1fd520867139e4f104a5ac57fcea57df2356eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a2459ba254f2fd66ca6bc851a1fd520867139e4f104a5ac57fcea57df2356eb","first_computed_at":"2026-05-17T23:43:07.180763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:07.180763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/UQMPX3dlQXt1DtjoQXSpCZzDEKGkKqpnKyrkjUUM/WEC1IdH1BugqsA3+hX1ySTodo5xvVJfDyCJUBVV2tqDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:07.181384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03887","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca41200e51aa6d29c3cb80c56966e3b20aea904c683318cc9f8015e126641748","sha256:e71eacfed887230562a1ac583e426f7fae663a37ee47e7ade4512851491a2fb8"],"state_sha256":"29555a62064c957eb1e02ee0439b8287fbd3dd22cb056a1955527953016c5a27"}