{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AFM22XDUJBNN6XQNCWHJIPMHH6","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":"486365a6e911143264d657d362766107e72f704a89707f818c264dd9b69b8f03","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-30T19:22:38Z","title_canon_sha256":"bb70d9d5db5fd740d377be4b51330c94fc7536b9529bd2b08a159d1baad98bc2"},"schema_version":"1.0","source":{"id":"0812.0164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0164","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0164v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0164","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"AFM22XDUJBNN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AFM22XDUJBNN6XQN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AFM22XDU","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:af5edd9bc464c7889cafd8ffaaa4b4b43bc8293d12f8b058701b144688eabf00","target":"graph","created_at":"2026-05-18T00:43:31Z","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":"The factor complexity of the infinite word $\\ubeta$ canonically associated to a non-simple Parry number $\\beta$ is studied. Our approach is based on the notion of special factors introduced by Berstel and Cassaigne. At first, we give a handy method for determining infinite left special branches; this method is applicable to a broad class of infinite words which are fixed points of a primitive substitution. In the second part of the article, we focus on infinite words $\\ubeta$ only. To complete the description of its special factors, we define and study $(a,b)$-maximal left special factors. Thi","authors_text":"Edita Pelantov\\'a, Karel Klouda","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-30T19:22:38Z","title":"Factor complexity of infinite words associated with non-simple Parry numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0164","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":"sha256:485e694e5cc08d39c52e71ca65c2298ec494b0b64a31df8cf5c052c6e160a832","target":"record","created_at":"2026-05-18T00:43:31Z","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":"486365a6e911143264d657d362766107e72f704a89707f818c264dd9b69b8f03","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-30T19:22:38Z","title_canon_sha256":"bb70d9d5db5fd740d377be4b51330c94fc7536b9529bd2b08a159d1baad98bc2"},"schema_version":"1.0","source":{"id":"0812.0164","kind":"arxiv","version":1}},"canonical_sha256":"0159ad5c74485adf5e0d158e943d873fa3287dd86f99017ee98b49af97a0800d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0159ad5c74485adf5e0d158e943d873fa3287dd86f99017ee98b49af97a0800d","first_computed_at":"2026-05-18T00:43:31.087541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:31.087541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OD8EcBEIaRzYtAjIXe/Aimp97j35+NoG7YYRY6u6c8esGxrrrDbA1c7gZ3oSPXk9ORRe7vzP1G2cB7VMWZc8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:31.087967Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:485e694e5cc08d39c52e71ca65c2298ec494b0b64a31df8cf5c052c6e160a832","sha256:af5edd9bc464c7889cafd8ffaaa4b4b43bc8293d12f8b058701b144688eabf00"],"state_sha256":"df24fc19bccafa6ac7d667d8ba8428b53f7f57d43d631cf40995a20db0088c19"}