{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LHXDEKMMP2U25TO5GEEVV4NLVU","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":"bd3488c3f82bcaf0ab19b8486ee4b17711ac05407d6fa363ce507125b654a421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-28T18:42:34Z","title_canon_sha256":"7e8a38374a47e2a74e708bf43072a43355bbc0ce0e5d261bf54fbec5a94e8894"},"schema_version":"1.0","source":{"id":"1808.09486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09486","created_at":"2026-05-17T23:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09486v2","created_at":"2026-05-17T23:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09486","created_at":"2026-05-17T23:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"LHXDEKMMP2U2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LHXDEKMMP2U25TO5","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LHXDEKMM","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:1a9b411a4040651673f5d4697dc034f27210cc44e078d540dcf6cc3b83af6131","target":"graph","created_at":"2026-05-17T23:41:46Z","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":"We prove inequalities relating the measures of maximal entropy of two patterns u,v where the extender set of u is contained in the extender set of v. Our main results are two generalizations of a Theorem of Meyerovitch; the first applies to all such v,w when G=Z, and the second to v,w with the same shape and any countable amenable finitely generated torsion-free G. As a consequence of our results we give new and simpler proofs of several facts about synchronizing subshifts and we answer a question of Climenhaga.","authors_text":"Felipe Garc\\'ia-Ramos, Ronnie Pavlov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-28T18:42:34Z","title":"Extender sets and measures of maximal entropy for subshifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09486","kind":"arxiv","version":2},"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":"sha256:705537c27bccd3b867dbb7d9e361e2153d296e81a869e72d0f56e5316d451de6","target":"record","created_at":"2026-05-17T23:41:46Z","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":"bd3488c3f82bcaf0ab19b8486ee4b17711ac05407d6fa363ce507125b654a421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-28T18:42:34Z","title_canon_sha256":"7e8a38374a47e2a74e708bf43072a43355bbc0ce0e5d261bf54fbec5a94e8894"},"schema_version":"1.0","source":{"id":"1808.09486","kind":"arxiv","version":2}},"canonical_sha256":"59ee32298c7ea9aecddd31095af1abad2d78f5b4966e4c7880e043b15d8de795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59ee32298c7ea9aecddd31095af1abad2d78f5b4966e4c7880e043b15d8de795","first_computed_at":"2026-05-17T23:41:46.138632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:46.138632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g9kOVSN4e4bOYS19qVhhhDpv9ClqeWJitsB1bhiutIQuCAUme0Gt0AOdgu43kpUuL5b50+P/K+yejJmQM8hWBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:46.139168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:705537c27bccd3b867dbb7d9e361e2153d296e81a869e72d0f56e5316d451de6","sha256:1a9b411a4040651673f5d4697dc034f27210cc44e078d540dcf6cc3b83af6131"],"state_sha256":"4247265672fa24c14dc05482726bf6d28c00879bec1709bcb909f67dee731011"}