{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H4BRIWLULT7MG7Y5JJ4Z5LKSEF","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":"2edc793bd54bedfc8b4cb973c15ed4ef7401ced9bc407d6c6d934964eab6d7cc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-13T00:23:49Z","title_canon_sha256":"8bad74050338fd6a2c89725222ce7ce701891f5bb41f6f919cdcefea83eefb71"},"schema_version":"1.0","source":{"id":"1212.3022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3022","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3022v2","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3022","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"H4BRIWLULT7M","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H4BRIWLULT7MG7Y5","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H4BRIWLU","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:478aa3e5d1c3f2a15c9e8473b6c308884d81f603fbfc8a428f74c1265d512f72","target":"graph","created_at":"2026-05-18T02:58:22Z","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":"We prove two results relating 3-manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3-manifold. If N has non-empty, toroidal boundary, and \\pi_1(N) is a Kaehler group, then N is the product of a torus with an interval. On the other hand, if N has either empty or toroidal boundary, and \\pi_1(N) is a quasi-projective group, then all the prime components of N are graph manifolds.","authors_text":"Alexander Suciu, Stefan Friedl","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-13T00:23:49Z","title":"Kaehler groups, quasi-projective groups, and 3-manifold groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3022","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":"sha256:6e4d94f8a98ec01fdea2e506069a50c1f8a1c7c1aad7b05443b8bee8336607db","target":"record","created_at":"2026-05-18T02:58:22Z","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":"2edc793bd54bedfc8b4cb973c15ed4ef7401ced9bc407d6c6d934964eab6d7cc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-13T00:23:49Z","title_canon_sha256":"8bad74050338fd6a2c89725222ce7ce701891f5bb41f6f919cdcefea83eefb71"},"schema_version":"1.0","source":{"id":"1212.3022","kind":"arxiv","version":2}},"canonical_sha256":"3f031459745cfec37f1d4a799ead52216a21bc075e5b4776dddcb8f6382eb468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f031459745cfec37f1d4a799ead52216a21bc075e5b4776dddcb8f6382eb468","first_computed_at":"2026-05-18T02:58:22.086106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:22.086106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zWXFFnTVOYv7qVjd1PTR4A3c2RHyAnGk2Qb+gJZIlEJOzJEfBT7FtRWfhrbM3PiU1DurWpwEE3ZQlxPExb2yCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:22.086614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e4d94f8a98ec01fdea2e506069a50c1f8a1c7c1aad7b05443b8bee8336607db","sha256:478aa3e5d1c3f2a15c9e8473b6c308884d81f603fbfc8a428f74c1265d512f72"],"state_sha256":"96923729add8506bae753acff503f65c0523aa0c1e1e9c7f70fbab64cfe9e6a8"}