{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FLSE5FAC26SJX5B7HMAQOZ2RVL","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":"c5fed9322e16df372171389654be42a5010b1cccba9f8efb6a73c14ab0b6022e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-18T12:54:00Z","title_canon_sha256":"faa666416627b61fb1656773ca44c9bc9963024f8ef6090b0001939937f7d917"},"schema_version":"1.0","source":{"id":"1402.4314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4314","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4314v1","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4314","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"pith_short_12","alias_value":"FLSE5FAC26SJ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FLSE5FAC26SJX5B7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FLSE5FAC","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:fb88350162e76422e488ec50ffa51b4c9301a4effbbc2b412076b71f03523873","target":"graph","created_at":"2026-05-18T02:58:44Z","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 study the expansions of real numbers in positive and negative real base as introduced by R\\'enyi, and Ito & Sadahiro, respectively. In particular, we compare the sets $\\mathbb{Z}_\\beta^+$ and $\\mathbb{Z}_{-\\beta}$ of nonnegative $\\beta$-integers and $(-\\beta)$-integers. We describe all bases $(\\pm\\beta)$ for which $\\mathbb{Z}_\\beta^+$ and $\\mathbb{Z}_{-\\beta}$ can be coded by infinite words which are fixed points of conjugated morphisms, and consequently have the same language. Moreover, we prove that this happens precisely for $\\beta$ with another interesting property, namely","authors_text":"Daniel Dombek, Tom\\'a\\v{s} V\\'avra, Zuzana Mas\\'akov\\'a","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-18T12:54:00Z","title":"Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4314","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:fdd5c6cb299beb20bfc615e65f8ff0a717a278ccb49ca77f9fd068650dfd64d3","target":"record","created_at":"2026-05-18T02:58:44Z","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":"c5fed9322e16df372171389654be42a5010b1cccba9f8efb6a73c14ab0b6022e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-18T12:54:00Z","title_canon_sha256":"faa666416627b61fb1656773ca44c9bc9963024f8ef6090b0001939937f7d917"},"schema_version":"1.0","source":{"id":"1402.4314","kind":"arxiv","version":1}},"canonical_sha256":"2ae44e9402d7a49bf43f3b01076751aacbc020bcf6b259b07b6d07f0b0b5dd2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ae44e9402d7a49bf43f3b01076751aacbc020bcf6b259b07b6d07f0b0b5dd2b","first_computed_at":"2026-05-18T02:58:44.243330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:44.243330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K000MDu4GpnZ7i33n3qzU4Pcl/Ki9UVrXp3XURyj5glsulq1NN+oFZ9uFLdOYZwGa7RG6inUpSQy8rEfwlIEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:44.243931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdd5c6cb299beb20bfc615e65f8ff0a717a278ccb49ca77f9fd068650dfd64d3","sha256:fb88350162e76422e488ec50ffa51b4c9301a4effbbc2b412076b71f03523873"],"state_sha256":"2507247db4d992288fef65276fd1c2706c5414172e185a6999fe7568f9159657"}