{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ASTC2GR4BVZQKX7I5YS73ISKLI","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":"953060ad6aeac9b6a04e7a0cbc7bfdc0385a80da485f44a5620da68441e034de","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T22:26:55Z","title_canon_sha256":"67b41ef6f1786732487bbd74310a41dc1d879eead40da0c84d064b78b6681fc0"},"schema_version":"1.0","source":{"id":"1104.1806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1806","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1806v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1806","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"ASTC2GR4BVZQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ASTC2GR4BVZQKX7I","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ASTC2GR4","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:19d2c1e7b8cbb62beea145ea14f252a61677326bff50c7cc2311b366928573cb","target":"graph","created_at":"2026-05-18T01:30:49Z","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 consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free groups has poly-context-free word problem, and conjecture that the converse also holds. We prove our conjecture for several classes of soluble groups, including metabelian groups and torsion-free soluble groups, and present progress towards resolving the conjecture for soluble groups in general. Some of the techniques introduced for proving languages not to b","authors_text":"Tara Brough","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T22:26:55Z","title":"Groups with poly-context-free word problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1806","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":"sha256:0a832f2bfa62c01eb9a81f8e3a7f32108b943a8aeb79869b584983751ee1a5d8","target":"record","created_at":"2026-05-18T01:30:49Z","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":"953060ad6aeac9b6a04e7a0cbc7bfdc0385a80da485f44a5620da68441e034de","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T22:26:55Z","title_canon_sha256":"67b41ef6f1786732487bbd74310a41dc1d879eead40da0c84d064b78b6681fc0"},"schema_version":"1.0","source":{"id":"1104.1806","kind":"arxiv","version":1}},"canonical_sha256":"04a62d1a3c0d73055fe8ee25fda24a5a18c48ada79968a6ed7bc7c4c35ed6675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04a62d1a3c0d73055fe8ee25fda24a5a18c48ada79968a6ed7bc7c4c35ed6675","first_computed_at":"2026-05-18T01:30:49.614843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.614843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yn1rHG4GJcjvbioFi7hGWCD8fU0QfaB82M6ziTi4x1T/ei1UWkFv9pDSL/VTEtTbScsP/2co9oZanGGfSafkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.615286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a832f2bfa62c01eb9a81f8e3a7f32108b943a8aeb79869b584983751ee1a5d8","sha256:19d2c1e7b8cbb62beea145ea14f252a61677326bff50c7cc2311b366928573cb"],"state_sha256":"c8cbb0d2095430bcac90137a87b09f5b3f6cd25e9524a7bb6074a8cfc2f5cc46"}