{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JW6ERYEP2TFO2A6N4YSMXYNMBI","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":"281c200f25f4920953198a2c8506fd8a4634ce281a1440f6058e7e4bcd4f2318","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-25T14:52:09Z","title_canon_sha256":"a4240d896eef0b999a0ccb9a7838eb9410a9969526aad276ef59e1b33ba831ce"},"schema_version":"1.0","source":{"id":"1804.09609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09609","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09609v1","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09609","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"JW6ERYEP2TFO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JW6ERYEP2TFO2A6N","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JW6ERYEP","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:d363d5335a8b106c52592095abaea776f433357b62fc13e28af99a4bf6670837","target":"graph","created_at":"2026-05-18T00:17:31Z","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":"Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then W is not a multiple context free language.","authors_text":"Robert H. Gilman, Robert P. Kropholler, Saul Schleimer","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-25T14:52:09Z","title":"Groups whose word problems are not semilinear"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09609","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:ccc3c5b746d82507bd334838cefc1a6bfa040a32846d26e2a615084e397aabbc","target":"record","created_at":"2026-05-18T00:17:31Z","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":"281c200f25f4920953198a2c8506fd8a4634ce281a1440f6058e7e4bcd4f2318","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-25T14:52:09Z","title_canon_sha256":"a4240d896eef0b999a0ccb9a7838eb9410a9969526aad276ef59e1b33ba831ce"},"schema_version":"1.0","source":{"id":"1804.09609","kind":"arxiv","version":1}},"canonical_sha256":"4dbc48e08fd4caed03cde624cbe1ac0a03dd7d9477f5bdc04f61750ba5a9a101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dbc48e08fd4caed03cde624cbe1ac0a03dd7d9477f5bdc04f61750ba5a9a101","first_computed_at":"2026-05-18T00:17:31.262096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:31.262096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AqIX4+1HSxnnVL661hdKn2LvjJwXaVGevXtocUx+GEqGqeTkFA8LTK87iEJQGwXlLi0J4e+1BvsMN6XTrtr+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:31.262605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccc3c5b746d82507bd334838cefc1a6bfa040a32846d26e2a615084e397aabbc","sha256:d363d5335a8b106c52592095abaea776f433357b62fc13e28af99a4bf6670837"],"state_sha256":"fc5c3c9216164eb1d3bfb7133a3f8d3bdbf9fa4c7a4f03377f2bff5d90152384"}