{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LGCDHTWB2N3FUTHU4O7MSEFPIW","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":"9dbeb00734f32b60b1c064c4831e4e2f0af945be5eaed9d16b5a67f3bfb953a0","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2024-03-14T18:47:11Z","title_canon_sha256":"2060aa11f414b76528043c803bfb91c4e5c214c9f0bed2633da5439a407e70a5"},"schema_version":"1.0","source":{"id":"2403.17964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.17964","created_at":"2026-07-05T10:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"2403.17964v2","created_at":"2026-07-05T10:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17964","created_at":"2026-07-05T10:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"LGCDHTWB2N3F","created_at":"2026-07-05T10:02:44Z"},{"alias_kind":"pith_short_16","alias_value":"LGCDHTWB2N3FUTHU","created_at":"2026-07-05T10:02:44Z"},{"alias_kind":"pith_short_8","alias_value":"LGCDHTWB","created_at":"2026-07-05T10:02:44Z"}],"graph_snapshots":[{"event_id":"sha256:39afd07ad74d9558b24764d0b443470796c039cf46d2a50daf65c95f39b95687","target":"graph","created_at":"2026-07-05T10:02:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.17964/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental groups of a hyperbolic 3-manifold.","authors_text":"Alina Vdovina, Olga Kharlampovich","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2024-03-14T18:47:11Z","title":"Quantifying separability in RAAGs via representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17964","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":"sha256:05d77c36cf833fd5a0bb8bc2f73f6242d939288162d46169801cc78850308e39","target":"record","created_at":"2026-07-05T10:02:44Z","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":"9dbeb00734f32b60b1c064c4831e4e2f0af945be5eaed9d16b5a67f3bfb953a0","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2024-03-14T18:47:11Z","title_canon_sha256":"2060aa11f414b76528043c803bfb91c4e5c214c9f0bed2633da5439a407e70a5"},"schema_version":"1.0","source":{"id":"2403.17964","kind":"arxiv","version":2}},"canonical_sha256":"598433cec1d3765a4cf4e3bec910af45a35df58a8dfe6108c02c154f10402fca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"598433cec1d3765a4cf4e3bec910af45a35df58a8dfe6108c02c154f10402fca","first_computed_at":"2026-07-05T10:02:44.539380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:44.539380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gv8qT51gJ5sp60gzZGjYqxZRwFJE9FUvvwpcccsO/B0ZwoByqGe75VBYpggGXUybmYSVYa4YzwHPvdX48jThDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:44.539856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.17964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05d77c36cf833fd5a0bb8bc2f73f6242d939288162d46169801cc78850308e39","sha256:39afd07ad74d9558b24764d0b443470796c039cf46d2a50daf65c95f39b95687"],"state_sha256":"949abe56d61210eb18a66061793598e25ea899459e79b2e245d04c834c60dcbb"}