{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WDQCJ5MV24YHUGPTZBGCYRQQHU","short_pith_number":"pith:WDQCJ5MV","schema_version":"1.0","canonical_sha256":"b0e024f595d7307a19f3c84c2c46103d3f56bb3d3ba30f904c5ab0044e76d501","source":{"kind":"arxiv","id":"1706.09483","version":1},"attestation_state":"computed","paper":{"title":"All properly ergodic Markov chains over a free group are orbit equivalent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.PR"],"primary_cat":"math.DS","authors_text":"Lewis Bowen","submitted_at":"2017-06-28T20:51:30Z","abstract_excerpt":"Previous work showed that all Bernoulli shifts over a free group are orbit-equivalent. This result is strengthened here by replacing Bernoulli shifts with the wider class of properly ergodic countable state Markov chains over a free group. A list of related open problems is provided."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.09483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-28T20:51:30Z","cross_cats_sorted":["math.OA","math.PR"],"title_canon_sha256":"ea9bfec4b1b112dd33fe0be6160a83f8421ffb16cd78a7d96803752be633b3c8","abstract_canon_sha256":"448f522cf20a470f1f81de0182d2bacb019aa1a082450e6b62250db8e69b308a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:14.963195Z","signature_b64":"tzC1CUuowTBjfAVlZrBh8nXfc4iuIGdh8TgIp8inJRfnpduFN8O0ZM1ZWFINR2PvY6Js1qAG0306wFiHAEa7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0e024f595d7307a19f3c84c2c46103d3f56bb3d3ba30f904c5ab0044e76d501","last_reissued_at":"2026-05-18T00:41:14.962464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:14.962464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All properly ergodic Markov chains over a free group are orbit equivalent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.PR"],"primary_cat":"math.DS","authors_text":"Lewis Bowen","submitted_at":"2017-06-28T20:51:30Z","abstract_excerpt":"Previous work showed that all Bernoulli shifts over a free group are orbit-equivalent. This result is strengthened here by replacing Bernoulli shifts with the wider class of properly ergodic countable state Markov chains over a free group. A list of related open problems is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09483","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.09483","created_at":"2026-05-18T00:41:14.962601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09483v1","created_at":"2026-05-18T00:41:14.962601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09483","created_at":"2026-05-18T00:41:14.962601+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDQCJ5MV24YH","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDQCJ5MV24YHUGPT","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDQCJ5MV","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU","json":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU.json","graph_json":"https://pith.science/api/pith-number/WDQCJ5MV24YHUGPTZBGCYRQQHU/graph.json","events_json":"https://pith.science/api/pith-number/WDQCJ5MV24YHUGPTZBGCYRQQHU/events.json","paper":"https://pith.science/paper/WDQCJ5MV"},"agent_actions":{"view_html":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU","download_json":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU.json","view_paper":"https://pith.science/paper/WDQCJ5MV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09483&json=true","fetch_graph":"https://pith.science/api/pith-number/WDQCJ5MV24YHUGPTZBGCYRQQHU/graph.json","fetch_events":"https://pith.science/api/pith-number/WDQCJ5MV24YHUGPTZBGCYRQQHU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU/action/storage_attestation","attest_author":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU/action/author_attestation","sign_citation":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU/action/citation_signature","submit_replication":"https://pith.science/pith/WDQCJ5MV24YHUGPTZBGCYRQQHU/action/replication_record"}},"created_at":"2026-05-18T00:41:14.962601+00:00","updated_at":"2026-05-18T00:41:14.962601+00:00"}