{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3SAJKXKFX4HXON4O2GYDWYORX5","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":"239cb499e6d3d31c634ee1ae8e3c680910763321c57623e7462713a25ef3479e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-20T20:53:38Z","title_canon_sha256":"e0ec299cba987d9c37531078a6776e16048e700c4dc1ed6a0bbb774729fb7383"},"schema_version":"1.0","source":{"id":"1804.07822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07822","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07822v3","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07822","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"3SAJKXKFX4HX","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3SAJKXKFX4HXON4O","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3SAJKXKF","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:bd0e2c7005f75f80bb93d3624e6f75f2fbef90307f6565ef2f39ec2a1edd7c4f","target":"graph","created_at":"2026-05-18T00:04:39Z","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 provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures and the boundary of higher dimensional generalized rotation sets. We also discuss the regularity of the localized entropy function on the boundary of the generalized rotation sets.","authors_text":"Christian Wolf, Yun Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-20T20:53:38Z","title":"A topological classification of locally constant potentials via zero-temperature measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07822","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:aa1932db602ae00fdc6f00c8e6d32cd0f8243f16d12e5f823fa3d2f446ff9fec","target":"record","created_at":"2026-05-18T00:04:39Z","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":"239cb499e6d3d31c634ee1ae8e3c680910763321c57623e7462713a25ef3479e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-20T20:53:38Z","title_canon_sha256":"e0ec299cba987d9c37531078a6776e16048e700c4dc1ed6a0bbb774729fb7383"},"schema_version":"1.0","source":{"id":"1804.07822","kind":"arxiv","version":3}},"canonical_sha256":"dc80955d45bf0f77378ed1b03b61d1bf466566a32bbed619ba3cfa4edb652238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc80955d45bf0f77378ed1b03b61d1bf466566a32bbed619ba3cfa4edb652238","first_computed_at":"2026-05-18T00:04:39.457124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:39.457124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anVeX0WkE//ynKeznBRk1G723gn1wCx6k3cmfltYDA6yBVE0QLQPSFrotjmpti1ymRLG1DV+dDvwHXb9OdmECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:39.457531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa1932db602ae00fdc6f00c8e6d32cd0f8243f16d12e5f823fa3d2f446ff9fec","sha256:bd0e2c7005f75f80bb93d3624e6f75f2fbef90307f6565ef2f39ec2a1edd7c4f"],"state_sha256":"f47fc8c0c6b5cf113aab585286b7ca352aa2199aa0281d6c6e57668198db8e75"}