{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YPODB2WXZD33GPW36AECIRWFUI","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":"e4a43795924e1a64adf03dc0f7d4ee359c6655e85dc08b3ddf7b39776f1e54e0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-04-06T14:53:23Z","title_canon_sha256":"f009eb5d58b66edfdb6956d1e28956d299b3c258d216e55de920eb93e029c310"},"schema_version":"1.0","source":{"id":"2104.02520","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02520","created_at":"2026-07-05T06:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02520v4","created_at":"2026-07-05T06:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02520","created_at":"2026-07-05T06:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"YPODB2WXZD33","created_at":"2026-07-05T06:09:03Z"},{"alias_kind":"pith_short_16","alias_value":"YPODB2WXZD33GPW3","created_at":"2026-07-05T06:09:03Z"},{"alias_kind":"pith_short_8","alias_value":"YPODB2WX","created_at":"2026-07-05T06:09:03Z"}],"graph_snapshots":[{"event_id":"sha256:04022e54cb0d12bc5f637f46fd828e4b63fe835d72b5322c8f2eb4eca9b14023","target":"graph","created_at":"2026-07-05T06:09:03Z","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/2104.02520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that $\\mathbb Q\\setminus\\mathbb Z$ is diophantine over $\\mathbb Q$, i.e., there is a polynomial $P(t,x_1,\\ldots,x_{n})\\in\\mathbb Z[t,x_1,\\ldots,x_{n}]$ such that for any rational number $t$ we have $$t\\not\\in\\mathbb Z\\iff \\exists x_1\\cdots\\exists x_{n}[P(t,x_1,\\ldots,x_{n})=0]$$ where variables range over $\\mathbb Q$, equivalently $$t\\in\\mathbb Z\\iff \\forall x_1\\cdots\\forall x_{n}[P(t,x_1,\\ldots,x_{n})\\not=0].$$ In this paper we prove that we may take $n=32$. Combining this with a result of Z.-W. Sun, we show that th","authors_text":"Geng-Rui Zhang, Zhi-Wei Sun","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-04-06T14:53:23Z","title":"$\\mathbb Q\\setminus\\mathbb Z$ is diophantine over $\\mathbb Q$ with 32 unknowns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02520","kind":"arxiv","version":4},"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":"sha256:591fbe37f4808b467cdb1360dff5dee0f3111c08f669573818fd33ac01023ede","target":"record","created_at":"2026-07-05T06:09:03Z","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":"e4a43795924e1a64adf03dc0f7d4ee359c6655e85dc08b3ddf7b39776f1e54e0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-04-06T14:53:23Z","title_canon_sha256":"f009eb5d58b66edfdb6956d1e28956d299b3c258d216e55de920eb93e029c310"},"schema_version":"1.0","source":{"id":"2104.02520","kind":"arxiv","version":4}},"canonical_sha256":"c3dc30ead7c8f7b33edbf0082446c5a2259d54e3de5bc1cc10f1b845d1de318d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3dc30ead7c8f7b33edbf0082446c5a2259d54e3de5bc1cc10f1b845d1de318d","first_computed_at":"2026-07-05T06:09:03.267581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:09:03.267581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xTXE7z6a6cbcTUdD70BhMmJILbOfL67WAPVmvs2Vseczf9eK6heEDLZ1exzr3dZ2wcUaHvwop6I9WnJjxiZ8DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:09:03.268016Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.02520","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:591fbe37f4808b467cdb1360dff5dee0f3111c08f669573818fd33ac01023ede","sha256:04022e54cb0d12bc5f637f46fd828e4b63fe835d72b5322c8f2eb4eca9b14023"],"state_sha256":"4a00bddb9579127f4ee89ba9357baa1b9d833d2a141e2def662849f350cc5463"}