{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VITHGKFZ3G3MA7I6JCP65OT5PU","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":"3e8a57fe1101abc49360995d6f321aee18fdb83b922fc6856e7ff5458d0f8e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-26T02:08:51Z","title_canon_sha256":"7fa3bae0feb1f9f530dfaa09b90d38e184ab875d668e76a7e49930e50a13af75"},"schema_version":"1.0","source":{"id":"2401.14598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.14598","created_at":"2026-07-05T07:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"2401.14598v1","created_at":"2026-07-05T07:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14598","created_at":"2026-07-05T07:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"VITHGKFZ3G3M","created_at":"2026-07-05T07:37:58Z"},{"alias_kind":"pith_short_16","alias_value":"VITHGKFZ3G3MA7I6","created_at":"2026-07-05T07:37:58Z"},{"alias_kind":"pith_short_8","alias_value":"VITHGKFZ","created_at":"2026-07-05T07:37:58Z"}],"graph_snapshots":[{"event_id":"sha256:a3b7708ed13afc0d597cd5ab357920f475e08960b345dffaa7092106d3fbdc2c","target":"graph","created_at":"2026-07-05T07:37:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.14598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\\Sigma_\\beta$ hierarchy. We focus on linear orderings. We show that at the $\\Sigma_1$ level all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the $\\Sigma_{\\alpha+2}$ level for any $\\alpha\\in\\omega_1^{ck}$ the set of linear orderings with generically or coarsely computable copies is $\\mathbf{\\Sigma}_1^1$-complete and therefore maximally complicated. This development is new ","authors_text":"David Gonzalez, Douglas Cenzer, Valentina Harizanov, Wesley Calvert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-26T02:08:51Z","title":"Generically Computable Linear Orderings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14598","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:dc533e795f44521d707b1b388c3df1c7a2e4e093e143545fc1e348c814af69f5","target":"record","created_at":"2026-07-05T07:37:58Z","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":"3e8a57fe1101abc49360995d6f321aee18fdb83b922fc6856e7ff5458d0f8e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-26T02:08:51Z","title_canon_sha256":"7fa3bae0feb1f9f530dfaa09b90d38e184ab875d668e76a7e49930e50a13af75"},"schema_version":"1.0","source":{"id":"2401.14598","kind":"arxiv","version":1}},"canonical_sha256":"aa267328b9d9b6c07d1e489feeba7d7d220713d04ed713a6b52c57363079b295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa267328b9d9b6c07d1e489feeba7d7d220713d04ed713a6b52c57363079b295","first_computed_at":"2026-07-05T07:37:58.879096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:37:58.879096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"leXcPEhWr3a7KbYduiDW9GjN14BIfMF6vHZ2QZs/ewZcsQ7sWRlSahR/qgTQQreqe/WTQ+zNwXUy/2Z4DDJxCA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:37:58.879562Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.14598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc533e795f44521d707b1b388c3df1c7a2e4e093e143545fc1e348c814af69f5","sha256:a3b7708ed13afc0d597cd5ab357920f475e08960b345dffaa7092106d3fbdc2c"],"state_sha256":"aac4b88fa3d6e31a27f0007867dd1ff8ea89a94c2630685dcc9f42ba333116bc"}