{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6TUF7DHGH3NVDP7OKZOXMNCG42","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":"b6a0256e81898bed8ec200f6a677a6022e7fa4c75f914d4b10021138cc94e96a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-11T22:48:20Z","title_canon_sha256":"19c181667856a9678f3e2e051fcdece4261ba40baf3d20d5fc37b8823702a51a"},"schema_version":"1.0","source":{"id":"1803.04060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04060","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04060v1","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04060","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"6TUF7DHGH3NV","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6TUF7DHGH3NVDP7O","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6TUF7DHG","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:401d0a01f82da15b67168d9263eead46ef37fac6bfd76d807977509139ee7491","target":"graph","created_at":"2026-05-18T00:21:32Z","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":"Let $(X_{A},\\sigma_{A})$ be a shift of finite type and $\\text{Aut}(\\sigma_{A})$ its corresponding automorphism group. Associated to $\\phi \\in \\text{Aut}(\\sigma_{A})$ are certain Lyapunov exponents $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ which describe asymptotic behavior of the sequence of coding ranges of $\\phi^{n}$. We give lower bounds on $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ in terms of the spectral radius of the corresponding action of $\\phi$ on the dimension group associated to $(X_{A},\\sigma_{A})$. We also give lower bounds on the topological entropy $h_{top}(\\phi)$ in terms of a distinguis","authors_text":"Scott Schmieding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-11T22:48:20Z","title":"Automorphisms of the shift: Lyapunov exponents, entropy, and the dimension representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04060","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":"sha256:2f76057fc637bd74ff2a3efd942577834f6f9a2459cff2d637c1d0038f7d1515","target":"record","created_at":"2026-05-18T00:21:32Z","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":"b6a0256e81898bed8ec200f6a677a6022e7fa4c75f914d4b10021138cc94e96a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-11T22:48:20Z","title_canon_sha256":"19c181667856a9678f3e2e051fcdece4261ba40baf3d20d5fc37b8823702a51a"},"schema_version":"1.0","source":{"id":"1803.04060","kind":"arxiv","version":1}},"canonical_sha256":"f4e85f8ce63edb51bfee565d763446e6877e5a8e019c487d31d8842c368c5bda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4e85f8ce63edb51bfee565d763446e6877e5a8e019c487d31d8842c368c5bda","first_computed_at":"2026-05-18T00:21:32.810342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:32.810342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"geK00edYXprt64IKwbkCFH+/vzefZLLhz3dej1Rzn3ZUb3HHmyhdqKFugV38ud1uFzyKfYS4ThlT0ZtIKEqZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:32.811246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f76057fc637bd74ff2a3efd942577834f6f9a2459cff2d637c1d0038f7d1515","sha256:401d0a01f82da15b67168d9263eead46ef37fac6bfd76d807977509139ee7491"],"state_sha256":"a78d4342736e129c513de39f89724263af63d6e1c371bab90bb107bc4a473012"}