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We first prove that for every 2-generic real X we have X' is not tt below X + 0'. We next prove that for every real X >=tt 0' there is a real Y such that Y + 0' =tt Y' =tt X. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on some cone."},"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":"0805.0005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-04-30T20:07:46Z","cross_cats_sorted":[],"title_canon_sha256":"707f1efbb3ea1c62b6a58eb8da63ca46369865ab711dcada517999454247a66a","abstract_canon_sha256":"0cb533f0a01b83ed7d1e5432853e3badf7142a80e0f51850abe0f7d143991773"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:13.461773Z","signature_b64":"PQS8+QXitbX7YaaBnie0r0zwBdxDFe/TlTIjuewnNih0j39Vi6MnEsIoBrUHdGggwYoh+mY9/uQfkBLyk8pGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ad64f428c376c746704b2aff6b2e7d631885ceeadd5388cf1780cddff4fdbf","last_reissued_at":"2026-05-18T04:20:13.461138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:13.461138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the truth-table degrees are fixed on some cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bernard A. Anderson","submitted_at":"2008-04-30T20:07:46Z","abstract_excerpt":"Let Dtt denote the set of truth-table degrees. A bijection p from Dtt to Dtt is an automorphism if for all truth-table degrees x and y we have x <=tt y if and only if p(x) <=tt p(y). We say an automorphism p is fixed on some cone if there is a degree b such that for all x >=tt b we have p(x) = x. We first prove that for every 2-generic real X we have X' is not tt below X + 0'. We next prove that for every real X >=tt 0' there is a real Y such that Y + 0' =tt Y' =tt X. Finally, we use this to demonstrate that every automorphism of the truth-table degrees is fixed on some cone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.0005","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":""},"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":"0805.0005","created_at":"2026-05-18T04:20:13.461217+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.0005v2","created_at":"2026-05-18T04:20:13.461217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0005","created_at":"2026-05-18T04:20:13.461217+00:00"},{"alias_kind":"pith_short_12","alias_value":"AKWWJ5BIYN3M","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"AKWWJ5BIYN3MORTQ","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"AKWWJ5BI","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2602.19750","citing_title":"Krylov Distribution and Universal Convergence of Quantum Fisher Information","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV","json":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV.json","graph_json":"https://pith.science/api/pith-number/AKWWJ5BIYN3MORTQJMVP62ZOPV/graph.json","events_json":"https://pith.science/api/pith-number/AKWWJ5BIYN3MORTQJMVP62ZOPV/events.json","paper":"https://pith.science/paper/AKWWJ5BI"},"agent_actions":{"view_html":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV","download_json":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV.json","view_paper":"https://pith.science/paper/AKWWJ5BI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.0005&json=true","fetch_graph":"https://pith.science/api/pith-number/AKWWJ5BIYN3MORTQJMVP62ZOPV/graph.json","fetch_events":"https://pith.science/api/pith-number/AKWWJ5BIYN3MORTQJMVP62ZOPV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/action/storage_attestation","attest_author":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/action/author_attestation","sign_citation":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/action/citation_signature","submit_replication":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/action/replication_record"}},"created_at":"2026-05-18T04:20:13.461217+00:00","updated_at":"2026-05-18T04:20:13.461217+00:00"}