{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5UNXH7ORQ6YCSRVCBHZETETKIA","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":"39c700514d9a4cedf02ca348baa8c609d143d6f44cf937a64c2c166ecae9970e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-27T21:22:25Z","title_canon_sha256":"3784762c878416a6d3b1d0ac2a3087042d47f634fa68b74ca7db17b022a891fb"},"schema_version":"1.0","source":{"id":"1401.7027","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7027","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7027v3","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7027","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"5UNXH7ORQ6YC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5UNXH7ORQ6YCSRVC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5UNXH7OR","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:51a3eaf59c4273c7044d24f62d327606155f28969aa18fbcd811901f5423ef12","target":"graph","created_at":"2026-05-17T23:54:07Z","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":"An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, $\\beta$-shift (transformation) and an intermediate $\\beta$-shift (transformation), for a fixed $\\beta \\in (1, 2)$. Specifically, a classification in terms of the kneading invariants of the linear maps $T_{\\beta,\\alpha} \\colon x \\mapsto \\beta x + \\alpha \\bmod 1$ for which the corresponding intermediate $\\beta$-shift is of finite type is given. This characterisation is then employed to construct a class of pairs $(\\beta,\\alpha)$ such that the intermediate $\\beta$-shift associated with $T_{\\beta, ","authors_text":"Bing Li, Tony Samuel, Tuomas Sahlsten","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-27T21:22:25Z","title":"Intermediate \\beta-shifts of finite type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7027","kind":"arxiv","version":3},"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":"sha256:9f3f9119cb2df5bac0e9ee1c8405bc1358b17395ea0ceaae046f3a95ef708f5a","target":"record","created_at":"2026-05-17T23:54:07Z","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":"39c700514d9a4cedf02ca348baa8c609d143d6f44cf937a64c2c166ecae9970e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-27T21:22:25Z","title_canon_sha256":"3784762c878416a6d3b1d0ac2a3087042d47f634fa68b74ca7db17b022a891fb"},"schema_version":"1.0","source":{"id":"1401.7027","kind":"arxiv","version":3}},"canonical_sha256":"ed1b73fdd187b02946a209f249926a4036c9b05bd757eb50cea2f44a4020ba1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed1b73fdd187b02946a209f249926a4036c9b05bd757eb50cea2f44a4020ba1f","first_computed_at":"2026-05-17T23:54:07.912840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:07.912840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqquUZkVvSv5VSuZOI1gayMHjedGJPXcjI8vS1xxhwa0qllDPaiffDeJfU4nwBoR13aPFR9fLb+A9/88vZ9EDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:07.913279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7027","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f3f9119cb2df5bac0e9ee1c8405bc1358b17395ea0ceaae046f3a95ef708f5a","sha256:51a3eaf59c4273c7044d24f62d327606155f28969aa18fbcd811901f5423ef12"],"state_sha256":"e4b3d5fb8306b768ae37bb0c8b2108bc18718d4f69a37d6a3a30e9eb1dab0b09"}