{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:REX7IEXITTGNUL6L3MFW5VHXNO","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":"06bf2f0be6c1140eaec44130b69ff8198b7327cd93391a2d82534755ce3b300d","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-16T02:20:13Z","title_canon_sha256":"53be63f514e040ef0e623d4d766d1142ac38f4c13ba4310f12f9677843495f31"},"schema_version":"1.0","source":{"id":"1607.04698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04698","created_at":"2026-05-18T00:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04698v2","created_at":"2026-05-18T00:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04698","created_at":"2026-05-18T00:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"REX7IEXITTGN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"REX7IEXITTGNUL6L","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"REX7IEXI","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:dc905d897ed2ba23fda9dc5a49fa7a84e49d7eb826e79c0faa6591194e160705","target":"graph","created_at":"2026-05-18T00:47:58Z","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":"For a positive integer $g$, let $\\mathrm{Sp}_{2g}(R)$ denote the group of $2g \\times 2g$ symplectic matrices over a ring $R$. Assume $g \\ge 2$. For a prime number $\\ell$, we give a self-contained proof that any closed subgroup of $\\mathrm{Sp}_{2g}(\\mathbb{Z}_\\ell)$ which surjects onto $\\mathrm{Sp}_{2g}(\\mathbb{Z}/\\ell\\mathbb{Z})$ must in fact equal all of $\\mathrm{Sp}_{2g}(\\mathbb{Z}_\\ell)$. The result and the method of proof are both motivated by group-theoretic considerations that arise in the study of Galois representations associated to abelian varieties.","authors_text":"Aaron Landesman, Ashvin Swaminathan, James Tao, Yujie Xu","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-16T02:20:13Z","title":"Lifting Subgroups of Symplectic Groups over $\\mathbb{Z} / \\ell \\mathbb{Z}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04698","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:f994ac0bc7bea9453b3257d46d5f45523e9f84f3b11d3cd0392411d4ecf683f9","target":"record","created_at":"2026-05-18T00:47:58Z","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":"06bf2f0be6c1140eaec44130b69ff8198b7327cd93391a2d82534755ce3b300d","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-16T02:20:13Z","title_canon_sha256":"53be63f514e040ef0e623d4d766d1142ac38f4c13ba4310f12f9677843495f31"},"schema_version":"1.0","source":{"id":"1607.04698","kind":"arxiv","version":2}},"canonical_sha256":"892ff412e89cccda2fcbdb0b6ed4f76b9d3db7591748491931da41bbd7fc5ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"892ff412e89cccda2fcbdb0b6ed4f76b9d3db7591748491931da41bbd7fc5ac9","first_computed_at":"2026-05-18T00:47:58.908627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:58.908627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jWruAPwImO4gZCpeOYgZQ6y1e+bosASzVZjyzVPpiPXxiAizyi1cA9L7ze8S5CyBVTFjzv418Seqs8iZqFdfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:58.909164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f994ac0bc7bea9453b3257d46d5f45523e9f84f3b11d3cd0392411d4ecf683f9","sha256:dc905d897ed2ba23fda9dc5a49fa7a84e49d7eb826e79c0faa6591194e160705"],"state_sha256":"412501053ef5c7defb641028a19076884c71ead2a6638d015c03a9fd5d837b8f"}