{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:35PLBM2JSCNBFP6R6JRLYM3MTJ","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":"db4a8b4b259fc0079591807e3a25855ebd56f0ecae715368f002efd0257560e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-03-30T23:25:28Z","title_canon_sha256":"05be8a13287eb5b7cc627ee96b837a5649793f448b4d23233868f0bff19d257f"},"schema_version":"1.0","source":{"id":"2203.16712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.16712","created_at":"2026-07-05T04:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.16712v1","created_at":"2026-07-05T04:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16712","created_at":"2026-07-05T04:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"35PLBM2JSCNB","created_at":"2026-07-05T04:10:15Z"},{"alias_kind":"pith_short_16","alias_value":"35PLBM2JSCNBFP6R","created_at":"2026-07-05T04:10:15Z"},{"alias_kind":"pith_short_8","alias_value":"35PLBM2J","created_at":"2026-07-05T04:10:15Z"}],"graph_snapshots":[{"event_id":"sha256:0edec6934cdaeccaa20f6bcf53655ea3b9e08d68892fd0b567ef6edb7dbd101f","target":"graph","created_at":"2026-07-05T04:10:15Z","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/2203.16712/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We adapt tools from the algebraic approach to constraint satisfaction problems to answer descriptive set theoretic questions about Borel CSPs. We show that if a structure $\\mathcal D$ does not have a Taylor polymorphism, then the corresponding Borel CSP is $\\mathbf{\\Sigma}^1_2$-complete. In particular, by the CSP Dichotomy Theorem, if $\\operatorname{CSP}(\\mathcal D)$ is $\\mathrm{NP}$-complete, then the Borel version, $\\operatorname{csp}_B(\\mathcal D)$, is $\\mathbf{\\Sigma}^1_2$-complete (assuming $\\mathrm{P}\\not=\\mathrm{NP}$). We also have partial converses, such as a descriptive analogue of th","authors_text":"Riley Thornton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-03-30T23:25:28Z","title":"An algebraic approach to Borel CSPs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16712","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":"sha256:6982a74f7a44db76c9c91c67a8124a35a5648b825cb6c7850b514703c056dd37","target":"record","created_at":"2026-07-05T04:10:15Z","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":"db4a8b4b259fc0079591807e3a25855ebd56f0ecae715368f002efd0257560e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-03-30T23:25:28Z","title_canon_sha256":"05be8a13287eb5b7cc627ee96b837a5649793f448b4d23233868f0bff19d257f"},"schema_version":"1.0","source":{"id":"2203.16712","kind":"arxiv","version":1}},"canonical_sha256":"df5eb0b349909a12bfd1f262bc336c9a4109a67d6698f56fb37ef367cbb51492","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df5eb0b349909a12bfd1f262bc336c9a4109a67d6698f56fb37ef367cbb51492","first_computed_at":"2026-07-05T04:10:15.322121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:15.322121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wPfEGshMipmlXYlxpyMT/4GvnAkhf0qGEhBep15moD1/ua6wfY1RHYcB7uZJbxHqaZULJtDftSy8eqTUXBe8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:15.322515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.16712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6982a74f7a44db76c9c91c67a8124a35a5648b825cb6c7850b514703c056dd37","sha256:0edec6934cdaeccaa20f6bcf53655ea3b9e08d68892fd0b567ef6edb7dbd101f"],"state_sha256":"b99caa2c14e51809ab2049d36603c95e2bc4c4e7b86d1b9892cfcdae3a3f72c5"}