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A variation of this definition was studied in 2002 by Komornik and Loreti, together with sequences called {\\em admissible sequences}. We show how a 1983 study of the first author gives both a result of Komornik and Loreti on the smallest admissible sequence on the set $\\{0, 1, >..., b\\}$, and a result of de Vries and Komornik (2007) on "},"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":"0712.0102","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-01T19:14:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"01323e9467c682e3f405b59ac832b9d478060e238b40f87743e65c2052444567","abstract_canon_sha256":"eccd57a72fefbe20b7802359937bb301805405cec5fae71a0b4939a545803761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:08.868848Z","signature_b64":"may7qdnsQc8gylMOEqPiPV1LVnnt/mgO5C7EyYOzMFpRHrdrf6nE+8zx0HwevPVqAQZDUdGAbpLdHR80plEMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf179ee13ce9f4c3b0e8f460c7294f4c9b984fbfecb88440d325c1bdd657dcad","last_reissued_at":"2026-05-18T02:16:08.867992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:08.867992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Univoque numbers and an avatar of Thue-Morse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Christiane Frougny, Jean-Paul Allouche","submitted_at":"2007-12-01T19:14:22Z","abstract_excerpt":"Univoque numbers are real numbers $\\lambda > 1$ such that the number 1 admits a unique expansion in base $\\lambda$, i.e., a unique expansion $1 = \\sum_{j \\geq 0} a_j \\lambda^{-(j+1)}$, with $a_j \\in \\{0, 1, ..., \\lceil \\lambda \\rceil -1\\}$ for every $j \\geq 0$. A variation of this definition was studied in 2002 by Komornik and Loreti, together with sequences called {\\em admissible sequences}. We show how a 1983 study of the first author gives both a result of Komornik and Loreti on the smallest admissible sequence on the set $\\{0, 1, >..., b\\}$, and a result of de Vries and Komornik (2007) on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0102","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0712.0102","created_at":"2026-05-18T02:16:08.868138+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.0102v2","created_at":"2026-05-18T02:16:08.868138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.0102","created_at":"2026-05-18T02:16:08.868138+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4LZ5YJ45H2M","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4LZ5YJ45H2MHMHI","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4LZ5YJ4","created_at":"2026-05-18T12:25:56.245647+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/X4LZ5YJ45H2MHMHI6RQMOKKPJS","json":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS.json","graph_json":"https://pith.science/api/pith-number/X4LZ5YJ45H2MHMHI6RQMOKKPJS/graph.json","events_json":"https://pith.science/api/pith-number/X4LZ5YJ45H2MHMHI6RQMOKKPJS/events.json","paper":"https://pith.science/paper/X4LZ5YJ4"},"agent_actions":{"view_html":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS","download_json":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS.json","view_paper":"https://pith.science/paper/X4LZ5YJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.0102&json=true","fetch_graph":"https://pith.science/api/pith-number/X4LZ5YJ45H2MHMHI6RQMOKKPJS/graph.json","fetch_events":"https://pith.science/api/pith-number/X4LZ5YJ45H2MHMHI6RQMOKKPJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS/action/storage_attestation","attest_author":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS/action/author_attestation","sign_citation":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS/action/citation_signature","submit_replication":"https://pith.science/pith/X4LZ5YJ45H2MHMHI6RQMOKKPJS/action/replication_record"}},"created_at":"2026-05-18T02:16:08.868138+00:00","updated_at":"2026-05-18T02:16:08.868138+00:00"}