{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CNQIWT7MY2ZFFEYB35RYRVL5EC","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":"2789f8927ceae0f7f3af465e239dc3ba6c3b9b7cccd349ceedf19aecbe083a8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-26T16:19:08Z","title_canon_sha256":"2a81742df99262046478fe849d8b2429459c6c6c136b168937944d9a2634f172"},"schema_version":"1.0","source":{"id":"1009.5105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5105","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5105v2","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5105","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"CNQIWT7MY2ZF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CNQIWT7MY2ZFFEYB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CNQIWT7M","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:df2c251ff56d54755d6c75929973c2e4a112641a7ee0dc62256371f744be3d5c","target":"graph","created_at":"2026-05-18T03:34:46Z","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":"In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms P_ret closed under composition and we show that a uniformly recurrent word with finite defect is an image of a rich (also called full) word under a morphism of class P_ret. This class is closely related to the well-known class P defined by Hof, Knill, and Simon; every morphism from P_ret is conjugate to a morphism of class P.","authors_text":"Edita Pelantov\\'a, Lubom\\'ira Balkov\\'a, \\v{S}t\\v{e}p\\'an Starosta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-26T16:19:08Z","title":"Infinite Words with Finite Defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5105","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":"sha256:5dee98b73af9e4fb2c904cf43c78e4ac6c009a4b4b269c15f32229a288ae67b3","target":"record","created_at":"2026-05-18T03:34:46Z","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":"2789f8927ceae0f7f3af465e239dc3ba6c3b9b7cccd349ceedf19aecbe083a8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-26T16:19:08Z","title_canon_sha256":"2a81742df99262046478fe849d8b2429459c6c6c136b168937944d9a2634f172"},"schema_version":"1.0","source":{"id":"1009.5105","kind":"arxiv","version":2}},"canonical_sha256":"13608b4fecc6b2529301df6388d57d208c7b52807e6421818a23f2942c6f65f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13608b4fecc6b2529301df6388d57d208c7b52807e6421818a23f2942c6f65f9","first_computed_at":"2026-05-18T03:34:46.561080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:46.561080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ydfoV4lcetuCJyqPJxxGJXUdAZFhCRMPoZAIlGOgJctwBTqKs19uD/MM8t59rlRiXMvv66J6wQHwFtUeF3+RAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:46.561646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dee98b73af9e4fb2c904cf43c78e4ac6c009a4b4b269c15f32229a288ae67b3","sha256:df2c251ff56d54755d6c75929973c2e4a112641a7ee0dc62256371f744be3d5c"],"state_sha256":"606afd9b70092f6f0a6a78211981abf19a0cef160e475fdfc8bd4b7c6cb8b814"}