{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:AKWWJ5BIYN3MORTQJMVP62ZOPV","short_pith_number":"pith:AKWWJ5BI","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"},"canonical_sha256":"02ad64f428c376c746704b2aff6b2e7d631885ceeadd5388cf1780cddff4fdbf","source":{"kind":"arxiv","id":"0805.0005","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.0005","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"0805.0005v2","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0005","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"AKWWJ5BIYN3M","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AKWWJ5BIYN3MORTQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AKWWJ5BI","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:AKWWJ5BIYN3MORTQJMVP62ZOPV","target":"record","payload":{"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"},"canonical_sha256":"02ad64f428c376c746704b2aff6b2e7d631885ceeadd5388cf1780cddff4fdbf","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"},"source_kind":"arxiv","source_id":"0805.0005","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyNIhHCjKq5BmUzmOfCHDYQgikuGbtU8D3kxccXu3niIZRDtVDZwBATjx3lVkERaCi1ADJmNiD9widnSHEOjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:38:09.681194Z"},"content_sha256":"dd898f2b7b30fe83cfdfc7656576481c1019df76d173e03412b11befd30238f4","schema_version":"1.0","event_id":"sha256:dd898f2b7b30fe83cfdfc7656576481c1019df76d173e03412b11befd30238f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:AKWWJ5BIYN3MORTQJMVP62ZOPV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECZSYIQnAJcNzHPdAWxqO5jRVQbJTLoQ2x9zoAaC0UoxEcKhu447901bd7iSwip2a+LlL6rDy2HuP3AUdOL7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:38:09.681858Z"},"content_sha256":"4bf242978a4ece4bf447e27ed5212e9b9731222d3e3a2c3fc72ee84aae69435a","schema_version":"1.0","event_id":"sha256:4bf242978a4ece4bf447e27ed5212e9b9731222d3e3a2c3fc72ee84aae69435a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/bundle.json","state_url":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T05:38:09Z","links":{"resolver":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV","bundle":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/bundle.json","state":"https://pith.science/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKWWJ5BIYN3MORTQJMVP62ZOPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AKWWJ5BIYN3MORTQJMVP62ZOPV","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":"0cb533f0a01b83ed7d1e5432853e3badf7142a80e0f51850abe0f7d143991773","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-04-30T20:07:46Z","title_canon_sha256":"707f1efbb3ea1c62b6a58eb8da63ca46369865ab711dcada517999454247a66a"},"schema_version":"1.0","source":{"id":"0805.0005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.0005","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"0805.0005v2","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0005","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"AKWWJ5BIYN3M","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AKWWJ5BIYN3MORTQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AKWWJ5BI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:4bf242978a4ece4bf447e27ed5212e9b9731222d3e3a2c3fc72ee84aae69435a","target":"graph","created_at":"2026-05-18T04:20:13Z","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":"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.","authors_text":"Bernard A. Anderson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-04-30T20:07:46Z","title":"Automorphisms of the truth-table degrees are fixed on some cone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.0005","kind":"arxiv","version":2},"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:dd898f2b7b30fe83cfdfc7656576481c1019df76d173e03412b11befd30238f4","target":"record","created_at":"2026-05-18T04:20:13Z","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":"0cb533f0a01b83ed7d1e5432853e3badf7142a80e0f51850abe0f7d143991773","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-04-30T20:07:46Z","title_canon_sha256":"707f1efbb3ea1c62b6a58eb8da63ca46369865ab711dcada517999454247a66a"},"schema_version":"1.0","source":{"id":"0805.0005","kind":"arxiv","version":2}},"canonical_sha256":"02ad64f428c376c746704b2aff6b2e7d631885ceeadd5388cf1780cddff4fdbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02ad64f428c376c746704b2aff6b2e7d631885ceeadd5388cf1780cddff4fdbf","first_computed_at":"2026-05-18T04:20:13.461138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:13.461138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQS8+QXitbX7YaaBnie0r0zwBdxDFe/TlTIjuewnNih0j39Vi6MnEsIoBrUHdGggwYoh+mY9/uQfkBLyk8pGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:13.461773Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.0005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd898f2b7b30fe83cfdfc7656576481c1019df76d173e03412b11befd30238f4","sha256:4bf242978a4ece4bf447e27ed5212e9b9731222d3e3a2c3fc72ee84aae69435a"],"state_sha256":"43ef3d54604960afcb77fe111323f18236f78fc76ed93fd67da8442c8c6397d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tSqduieyBkbwxywppw3489Pv+EnAYg4qclp/G74fjmUvScIMXcnxbS7ZjUqk+tJKrIr5SzNeXPvXm3tmAdtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:38:09.685674Z","bundle_sha256":"020b384bde011837a84f6ffa5544041c9cf31239080dc71682c65a43f03ee2be"}}