{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5QEDTSRZV2NP5EFJHAQ27XBMOB","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":"989103001b4ca63dfdda294b61f1568a3bfdac94cc7771f1998db92c2cbe91ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-01-10T01:46:24Z","title_canon_sha256":"9daa51b252c35882a01995275d630dabb1d887125b47323c6fa7ce5f541b2294"},"schema_version":"1.0","source":{"id":"1501.02299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02299","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02299v1","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02299","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"5QEDTSRZV2NP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5QEDTSRZV2NP5EFJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5QEDTSRZ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:5c73eec10551dd421b3c447759416b7140324d496cf09567c4789f4bed536c86","target":"graph","created_at":"2026-05-18T02:29:38Z","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":"A set is low if A' \\le_T HALT. A set is superlow if A' \\le_tt HALT. A set is superduperlow if A' \\le_btt HALT. While it was known that any superduperlow is decidable it does not seem to be well known. We include two unpublished proofs of this result: One from Carl Jockush and one from Frank Stephan.","authors_text":"William Gasarch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-01-10T01:46:24Z","title":"Low, Superlow, and Superduperlow Sets: An Exposition of a Known But Not Well-Known Result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02299","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:f0dc34cdb2c2cd4989523bd4b095a13fb99269316e1b10b3f93f62f1867b3fe7","target":"record","created_at":"2026-05-18T02:29:38Z","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":"989103001b4ca63dfdda294b61f1568a3bfdac94cc7771f1998db92c2cbe91ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-01-10T01:46:24Z","title_canon_sha256":"9daa51b252c35882a01995275d630dabb1d887125b47323c6fa7ce5f541b2294"},"schema_version":"1.0","source":{"id":"1501.02299","kind":"arxiv","version":1}},"canonical_sha256":"ec0839ca39ae9afe90a93821afdc2c7040e1ff267995e2a084718584d2a76cc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec0839ca39ae9afe90a93821afdc2c7040e1ff267995e2a084718584d2a76cc4","first_computed_at":"2026-05-18T02:29:38.325788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:38.325788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNJMMPESpYG8N86g2b9l+zWHQn82WDivCioSoffnb584cNm13boLJjdQtEjYGpwdWPEBdDqaLiODzJFzgKv5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:38.326299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0dc34cdb2c2cd4989523bd4b095a13fb99269316e1b10b3f93f62f1867b3fe7","sha256:5c73eec10551dd421b3c447759416b7140324d496cf09567c4789f4bed536c86"],"state_sha256":"4d8eec60e441480ea34c80e717225f8adf7eb406c2f74f0d36251eba36404470"}