{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:OCOECN22PQWEN3AXFSNBMT7KBR","short_pith_number":"pith:OCOECN22","schema_version":"1.0","canonical_sha256":"709c41375a7c2c46ec172c9a164fea0c6acf0581e1305024d778bd75fb92cf5e","source":{"kind":"arxiv","id":"0708.4387","version":1},"attestation_state":"computed","paper":{"title":"Conjugates of characteristic Sturmian words generated by morphisms","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen","submitted_at":"2007-08-31T16:26:57Z","abstract_excerpt":"This article is concerned with characteristic Sturmian words of slope $\\alpha$ and $1-\\alpha$ (denoted by $c_\\alpha$ and $c_{1-\\alpha}$ respectively), where $\\alpha \\in (0,1)$ is an irrational number such that $\\alpha = [0;1+d_1,\\bar{d_2,...,d_n}]$ with $d_n \\geq d_1 \\geq 1$. It is known that both $c_\\alpha$ and $c_{1-\\alpha}$ are fixed points of non-trivial (standard) morphisms $\\sigma$ and $\\hat{\\sigma}$, respectively, if and only if $\\alpha$ has a continued fraction expansion as above. Accordingly, such words $c_\\alpha$ and $c_{1-\\alpha}$ are generated by the respective morphisms $\\sigma$ a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0708.4387","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-08-31T16:26:57Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ed223d83ca333d74077c32f7c27ff3f5c0a5c98ae5f2acebac6e3c0c7c9d0db3","abstract_canon_sha256":"1072d991571634402c74281bb72b510e0a33facbf1fb221a32b6905fdeda36d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:23:15.757204Z","signature_b64":"Y3aPrpQMcVNd3CiPQWvnV5zixuj7RlfsXz41LkmZzgdwiIWAZfmJpSTYpB6oJqrcuLbr49hoxDryPCM552RJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"709c41375a7c2c46ec172c9a164fea0c6acf0581e1305024d778bd75fb92cf5e","last_reissued_at":"2026-07-04T17:23:15.756819Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:23:15.756819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugates of characteristic Sturmian words generated by morphisms","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen","submitted_at":"2007-08-31T16:26:57Z","abstract_excerpt":"This article is concerned with characteristic Sturmian words of slope $\\alpha$ and $1-\\alpha$ (denoted by $c_\\alpha$ and $c_{1-\\alpha}$ respectively), where $\\alpha \\in (0,1)$ is an irrational number such that $\\alpha = [0;1+d_1,\\bar{d_2,...,d_n}]$ with $d_n \\geq d_1 \\geq 1$. It is known that both $c_\\alpha$ and $c_{1-\\alpha}$ are fixed points of non-trivial (standard) morphisms $\\sigma$ and $\\hat{\\sigma}$, respectively, if and only if $\\alpha$ has a continued fraction expansion as above. Accordingly, such words $c_\\alpha$ and $c_{1-\\alpha}$ are generated by the respective morphisms $\\sigma$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.4387","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0708.4387/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0708.4387","created_at":"2026-07-04T17:23:15.756881+00:00"},{"alias_kind":"arxiv_version","alias_value":"0708.4387v1","created_at":"2026-07-04T17:23:15.756881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.4387","created_at":"2026-07-04T17:23:15.756881+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCOECN22PQWE","created_at":"2026-07-04T17:23:15.756881+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCOECN22PQWEN3AX","created_at":"2026-07-04T17:23:15.756881+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCOECN22","created_at":"2026-07-04T17:23:15.756881+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR","json":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR.json","graph_json":"https://pith.science/api/pith-number/OCOECN22PQWEN3AXFSNBMT7KBR/graph.json","events_json":"https://pith.science/api/pith-number/OCOECN22PQWEN3AXFSNBMT7KBR/events.json","paper":"https://pith.science/paper/OCOECN22"},"agent_actions":{"view_html":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR","download_json":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR.json","view_paper":"https://pith.science/paper/OCOECN22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0708.4387&json=true","fetch_graph":"https://pith.science/api/pith-number/OCOECN22PQWEN3AXFSNBMT7KBR/graph.json","fetch_events":"https://pith.science/api/pith-number/OCOECN22PQWEN3AXFSNBMT7KBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR/action/storage_attestation","attest_author":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR/action/author_attestation","sign_citation":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR/action/citation_signature","submit_replication":"https://pith.science/pith/OCOECN22PQWEN3AXFSNBMT7KBR/action/replication_record"}},"created_at":"2026-07-04T17:23:15.756881+00:00","updated_at":"2026-07-04T17:23:15.756881+00:00"}