{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VPF5V2T45N6GWO6SHRSL3XOXLW","short_pith_number":"pith:VPF5V2T4","schema_version":"1.0","canonical_sha256":"abcbdaea7ceb7c6b3bd23c64bdddd75d84fb1ca2f8a0ae133ec24ed6ecc21650","source":{"kind":"arxiv","id":"1908.05381","version":2},"attestation_state":"computed","paper":{"title":"A tractable case of the Turing automorphism problem: bi-uniformly $E_0$-invariant Cantor homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bj{\\o}rn Kjos-Hanssen","submitted_at":"2019-08-15T00:39:33Z","abstract_excerpt":"A function $F:2^\\omega\\to 2^\\omega$ is an $E_0$-isomorphism if for all $x,y\\in 2^\\omega$, we have $xE_0y\\iff f(x)E_0 f(y)$, where $xE_0y\\iff(\\exists a)(\\forall n\\ge b) x(n)=y(n)$. If such witnesses $a$ for $xE_0 y$ and for $f(x)E_0 f(y)$ depend on each other but not on $x$, $y$, then $F$ is called bi-uniform. It is shown that a homeomorphism of Cantor space which is a bi-uniform $E_0$-isomorphism can induce only the trivial automorphism of the Turing degrees."},"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":"1908.05381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-15T00:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"3d853d7cfa249e3b6bccc85038fc33ce2cfa5c17391c75b16929a46921ce7e40","abstract_canon_sha256":"8bfacee28041bbfc36d1594dbb66d61357edd716b9ca2f30efb259ce08d69842"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:31:21.707966Z","signature_b64":"TedU+5V3CQWZX0Imj6YkNvwAMwBYtgkrDb4Ix/0Od4PkX87C4eawGyxahPSGt/1Kr40UFEE5FNwPgh9Bwp8CBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abcbdaea7ceb7c6b3bd23c64bdddd75d84fb1ca2f8a0ae133ec24ed6ecc21650","last_reissued_at":"2026-07-05T01:31:21.707559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:31:21.707559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A tractable case of the Turing automorphism problem: bi-uniformly $E_0$-invariant Cantor homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bj{\\o}rn Kjos-Hanssen","submitted_at":"2019-08-15T00:39:33Z","abstract_excerpt":"A function $F:2^\\omega\\to 2^\\omega$ is an $E_0$-isomorphism if for all $x,y\\in 2^\\omega$, we have $xE_0y\\iff f(x)E_0 f(y)$, where $xE_0y\\iff(\\exists a)(\\forall n\\ge b) x(n)=y(n)$. If such witnesses $a$ for $xE_0 y$ and for $f(x)E_0 f(y)$ depend on each other but not on $x$, $y$, then $F$ is called bi-uniform. It is shown that a homeomorphism of Cantor space which is a bi-uniform $E_0$-isomorphism can induce only the trivial automorphism of the Turing degrees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05381","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05381/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.05381","created_at":"2026-07-05T01:31:21.707615+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05381v2","created_at":"2026-07-05T01:31:21.707615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05381","created_at":"2026-07-05T01:31:21.707615+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPF5V2T45N6G","created_at":"2026-07-05T01:31:21.707615+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPF5V2T45N6GWO6S","created_at":"2026-07-05T01:31:21.707615+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPF5V2T4","created_at":"2026-07-05T01:31:21.707615+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/VPF5V2T45N6GWO6SHRSL3XOXLW","json":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW.json","graph_json":"https://pith.science/api/pith-number/VPF5V2T45N6GWO6SHRSL3XOXLW/graph.json","events_json":"https://pith.science/api/pith-number/VPF5V2T45N6GWO6SHRSL3XOXLW/events.json","paper":"https://pith.science/paper/VPF5V2T4"},"agent_actions":{"view_html":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW","download_json":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW.json","view_paper":"https://pith.science/paper/VPF5V2T4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05381&json=true","fetch_graph":"https://pith.science/api/pith-number/VPF5V2T45N6GWO6SHRSL3XOXLW/graph.json","fetch_events":"https://pith.science/api/pith-number/VPF5V2T45N6GWO6SHRSL3XOXLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW/action/storage_attestation","attest_author":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW/action/author_attestation","sign_citation":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW/action/citation_signature","submit_replication":"https://pith.science/pith/VPF5V2T45N6GWO6SHRSL3XOXLW/action/replication_record"}},"created_at":"2026-07-05T01:31:21.707615+00:00","updated_at":"2026-07-05T01:31:21.707615+00:00"}