{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D3WTZECXWOR7ATZPXKX5VAUEUC","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":"9dd4a7fee82f8ca5084bf2327e341b4dad334879dbcb35c5f0ff6510ef9946ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-02-09T18:15:39Z","title_canon_sha256":"40bad60f0395d22e19c8f3ab944f1be779457e4b567b020d1de4e27f1f3893aa"},"schema_version":"1.0","source":{"id":"1002.1934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1934","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1934v1","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1934","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"D3WTZECXWOR7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D3WTZECXWOR7ATZP","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D3WTZECX","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:582bdb62dab3ce939a937e1c0859d4a47572461db81d8d7121e04a262ac59914","target":"graph","created_at":"2026-05-18T04:16:12Z","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":"For a group $H$ and a subset $X$ of $H$, we let ${}^HX$ denote the set $\\{hxh^{-1} \\mid h \\in H, x \\in X\\}$, and when $X$ is a free-generating set of $H$, we say that the set ${}^HX$ is a Whitehead subset of $H$.\n  For a group $F$ and an element $r$ of $F$, we say that $r$ is Cohen-Lyndon aspherical in $F$ if ${}^F\\{r\\}$ is a Whitehead subset of the subgroup of $F$ that is generated by ${}^F\\{r\\}$.\n  In 1963, D. E. Cohen and R. C. Lyndon independently showed that in each free group each non-trivial element is Cohen-Lyndon aspherical.\n  In 1987, M. Edjvet and J. Howie showed that if $A$ and $B$","authors_text":"Peter A. Linnell, Warren Dicks, Yago Antol\\'in","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-02-09T18:15:39Z","title":"On the local-indicability Cohen-Lyndon Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1934","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":"sha256:1f2e12f2290a5916ff4ab409ce3aa7f45e411855af7af1bee8353e1cef21fc14","target":"record","created_at":"2026-05-18T04:16:12Z","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":"9dd4a7fee82f8ca5084bf2327e341b4dad334879dbcb35c5f0ff6510ef9946ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-02-09T18:15:39Z","title_canon_sha256":"40bad60f0395d22e19c8f3ab944f1be779457e4b567b020d1de4e27f1f3893aa"},"schema_version":"1.0","source":{"id":"1002.1934","kind":"arxiv","version":1}},"canonical_sha256":"1eed3c9057b3a3f04f2fbaafda8284a097cd39d30dffd33efd49fd3ed466aa1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eed3c9057b3a3f04f2fbaafda8284a097cd39d30dffd33efd49fd3ed466aa1b","first_computed_at":"2026-05-18T04:16:12.242476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:12.242476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uakf+EbBlobknwUnFN9HjQToNidt9IdMEQg7ZlI9705S1hyq8HNzMicSWe5qcoMMuvofErQ4L8dPS3nPXMKLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:12.242857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f2e12f2290a5916ff4ab409ce3aa7f45e411855af7af1bee8353e1cef21fc14","sha256:582bdb62dab3ce939a937e1c0859d4a47572461db81d8d7121e04a262ac59914"],"state_sha256":"f89cf3f5efc2dd565a8cfe898df43b4911a41b8da707a222d07de3bc71fa418c"}