{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S6OXBRDWBZOQULK2ZX6TW7XR2F","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":"da06aea6a8e9ea52f7c9a0b70823bf608d5db4df8aa66e1a14f9072c359fc579","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-20T05:32:35Z","title_canon_sha256":"87f8c9e69f53cbb24b7a3749242ce23097d5a7f8dd916459e81842030e48ce4a"},"schema_version":"1.0","source":{"id":"1703.06609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06609","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06609v1","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06609","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"S6OXBRDWBZOQ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S6OXBRDWBZOQULK2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S6OXBRDW","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:810b76c3915844040513ca92501fb66ed5a1b79bafe399d3a4dc7a533906a4f0","target":"graph","created_at":"2026-05-18T00:48:22Z","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 fundamental groups of compact 3-manifolds are known to be residually finite. Feng Luo conjectured that a stronger statement is true, by only allowing finite groups of the form $PGL(2,R),$ where $R$ is some finite commutative ring with identity. We give an equivalent formulation of Luo's conjecture via faithful representations and provide various examples and a counterexample.","authors_text":"Montek Gill, Stefan Friedl, Stephan Tillmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-20T05:32:35Z","title":"Linear representations of 3-manifold groups over rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06609","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:a3e8aff708e3bbba20ef0c5376f23d919a7a67a759b1211c59b3ebe1fe288eaf","target":"record","created_at":"2026-05-18T00:48:22Z","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":"da06aea6a8e9ea52f7c9a0b70823bf608d5db4df8aa66e1a14f9072c359fc579","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-20T05:32:35Z","title_canon_sha256":"87f8c9e69f53cbb24b7a3749242ce23097d5a7f8dd916459e81842030e48ce4a"},"schema_version":"1.0","source":{"id":"1703.06609","kind":"arxiv","version":1}},"canonical_sha256":"979d70c4760e5d0a2d5acdfd3b7ef1d1533d05338693a82dd79be280e02baabf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979d70c4760e5d0a2d5acdfd3b7ef1d1533d05338693a82dd79be280e02baabf","first_computed_at":"2026-05-18T00:48:22.237041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:22.237041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLtsOa6UcAfNNr5MbJzViN2vY4bt9RDhALWFZM8fvFygqaasaeTP9BvFH57vRRCDJGH9s+JJACOrUTIA4bSQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:22.237799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e8aff708e3bbba20ef0c5376f23d919a7a67a759b1211c59b3ebe1fe288eaf","sha256:810b76c3915844040513ca92501fb66ed5a1b79bafe399d3a4dc7a533906a4f0"],"state_sha256":"cc27798e09d5036605834c03e03fe520094765d82a3535384480ded72424e145"}