{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MTCNSVESXIQLJECX2YB5IFWEJD","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":"ff376a4e49de103a6274dc53f5b9e074e19e00e7093fb307b6aa8d1a7801bb7d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-14T15:19:05Z","title_canon_sha256":"4835801060e523d7b4d38e7d73c9b4cc2c066e6b6d6dbf2ef17561a29427d4d0"},"schema_version":"1.0","source":{"id":"1510.04144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04144","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04144v2","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04144","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"MTCNSVESXIQL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTCNSVESXIQLJECX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTCNSVES","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:a8554046e1bf8c77863e34fca9dfb2d526a4ebd8fed573d9af00f8d1f880567d","target":"graph","created_at":"2026-05-18T00:01:01Z","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":"The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group.","authors_text":"D.B. McReynolds, Larsen Louder, Priyam Patel","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-14T15:19:05Z","title":"Zariski Closures and Subgroup Separability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04144","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:ac7f6ee7e4004d1f2f40a97fae2a2f9ccfc4579252cc9c6420308fe049f2cf25","target":"record","created_at":"2026-05-18T00:01:01Z","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":"ff376a4e49de103a6274dc53f5b9e074e19e00e7093fb307b6aa8d1a7801bb7d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-14T15:19:05Z","title_canon_sha256":"4835801060e523d7b4d38e7d73c9b4cc2c066e6b6d6dbf2ef17561a29427d4d0"},"schema_version":"1.0","source":{"id":"1510.04144","kind":"arxiv","version":2}},"canonical_sha256":"64c4d95492ba20b49057d603d416c448ed085d3287e3c8240a4983ed091cc954","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64c4d95492ba20b49057d603d416c448ed085d3287e3c8240a4983ed091cc954","first_computed_at":"2026-05-18T00:01:01.014548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:01.014548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aUJhKqWfevZoaMZ628tJwc7gjkfe52JqSEWca7EXHRVxT1R/AqSLb7L+nMZsLIfwPGeM2t/ojLoACriP9rWCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:01.015027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac7f6ee7e4004d1f2f40a97fae2a2f9ccfc4579252cc9c6420308fe049f2cf25","sha256:a8554046e1bf8c77863e34fca9dfb2d526a4ebd8fed573d9af00f8d1f880567d"],"state_sha256":"2fbb5dc66235f76770159630406334c7a1adcb10bccfd2d7e44c8b5f76a21f9c"}