{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JGIJYF2FDMVTSNAZIQILWCULNQ","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":"5c899121eb38cec966e046f3ecc6ec682b16b946881f62dab8beffa11618293e","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2011-08-18T03:52:46Z","title_canon_sha256":"02add61f458057ecc7598b2d36c7a4fae9a868c7a98449301a6bdf51c3cbd9d0"},"schema_version":"1.0","source":{"id":"1108.3622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3622","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3622v1","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3622","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"pith_short_12","alias_value":"JGIJYF2FDMVT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JGIJYF2FDMVTSNAZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JGIJYF2F","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:2545d08f42a17933cd96387b806fe7d357608176c00e758159c0942c50f678c8","target":"graph","created_at":"2026-05-18T04:15:15Z","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":"An infinte word  w  avoids a pattern  p  with the involution  t  if there is no substitution for the variables in  p  and no involution  t  such that the resulting word is a factor of  w.   We investigate the avoidance of patterns with respect to the size of the alphabet. For example, it is shown that the pattern  a t(a) a  can be avoided over three letters but not two letters, whereas it is well known that  a a a  is avoidable over two letters.","authors_text":"Bastian Bischoff (Institute for Formal Methods in Computer Science, Dirk Nowotka (Institute for Formal Methods in Computer Science, Universit\\\"at Stuttgart)","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2011-08-18T03:52:46Z","title":"Pattern Avoidability with Involution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3622","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":"sha256:66dbb239d6be76c7e1e46239534bbfeb42c5f95d674cc5431d51a59d2a9bdd27","target":"record","created_at":"2026-05-18T04:15:15Z","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":"5c899121eb38cec966e046f3ecc6ec682b16b946881f62dab8beffa11618293e","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2011-08-18T03:52:46Z","title_canon_sha256":"02add61f458057ecc7598b2d36c7a4fae9a868c7a98449301a6bdf51c3cbd9d0"},"schema_version":"1.0","source":{"id":"1108.3622","kind":"arxiv","version":1}},"canonical_sha256":"49909c17451b2b3934194410bb0a8b6c33423c051fafd98bd0861a42146577d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49909c17451b2b3934194410bb0a8b6c33423c051fafd98bd0861a42146577d7","first_computed_at":"2026-05-18T04:15:15.720818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:15.720818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/B3wHYGbeuYJXSbr01L5/EifpI6S0LS4XzLzigWFrFoIdfiYuVdpw7hQDx6Ce8SCLElQBmbR/GuaF2tEjHSWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:15.721614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66dbb239d6be76c7e1e46239534bbfeb42c5f95d674cc5431d51a59d2a9bdd27","sha256:2545d08f42a17933cd96387b806fe7d357608176c00e758159c0942c50f678c8"],"state_sha256":"29d833887d2678c6d7d281e64cc4c122c95d2bec62f013393330f6c15ccd2dc2"}