{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U6ZG6L6LD2ZGMHXR6XGEMJHDOB","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":"a4ef73bf5327cb86ec584fc8e4e1c7a174a2fdd9e0e3b6847882bfbe8f4acd48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-26T14:14:45Z","title_canon_sha256":"b9d62c61e4187170278f8de8f3e15b7720581520e815f53b7ab1d67b4d8166ac"},"schema_version":"1.0","source":{"id":"1602.08331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08331","created_at":"2026-05-18T01:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08331v1","created_at":"2026-05-18T01:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08331","created_at":"2026-05-18T01:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"U6ZG6L6LD2ZG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U6ZG6L6LD2ZGMHXR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U6ZG6L6L","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:8133ed4aec27588479b1fd3d519374f2bec14f062f4c9ec2221da82b48ac00ca","target":"graph","created_at":"2026-05-18T01:19:56Z","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 construct inhomogenous Markov measures for which the shift is of Kreiger type ${\\rm III}_{1}$. These measures are fully supported on a toplogical markov shift space of the hyperbolic toral automorphism $f(x,y)=\\left(\\{x+y\\},x\\right):\\mathbb{T}^{2}\\to\\mathbb{T}^{2}$ and are used in a subsequent paper in the construction of $C^{1}$ Anosov diffeomorphisms of $\\mathbb{T}^{2}$ without an absolutely continuous invariant measure.","authors_text":"Zemer Kosloff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-26T14:14:45Z","title":"Examples of type ${\\rm III}_{1}$ inhomogenous Markov shifts supported on topological Markov shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08331","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":"sha256:20584c987e3b63814a0296b06a5027781754331ecac0734f87aa02a7a174426f","target":"record","created_at":"2026-05-18T01:19:56Z","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":"a4ef73bf5327cb86ec584fc8e4e1c7a174a2fdd9e0e3b6847882bfbe8f4acd48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-26T14:14:45Z","title_canon_sha256":"b9d62c61e4187170278f8de8f3e15b7720581520e815f53b7ab1d67b4d8166ac"},"schema_version":"1.0","source":{"id":"1602.08331","kind":"arxiv","version":1}},"canonical_sha256":"a7b26f2fcb1eb2661ef1f5cc4624e3704a75ba1c75526c3300043f31db53b78b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7b26f2fcb1eb2661ef1f5cc4624e3704a75ba1c75526c3300043f31db53b78b","first_computed_at":"2026-05-18T01:19:56.338025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:56.338025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hwu+OWnonR6um2rWq+G6kcJ1RgT5xjwViQUpXLCiZNbSY10a26wgiUFMSR0wCqeACH131yw4YVtsHaKeHkJODw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:56.338551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20584c987e3b63814a0296b06a5027781754331ecac0734f87aa02a7a174426f","sha256:8133ed4aec27588479b1fd3d519374f2bec14f062f4c9ec2221da82b48ac00ca"],"state_sha256":"93ee8fe9bc9458d3c0f5c1193b8b76f5e40bab9c864708ec9baa6d0cf1678309"}