{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KAVA7J3XYXMJRJARRRQBRWNHZ3","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":"f2c9c4e3fb686265717285c06ad87efe65cd2f2f8d0a96fdea7b781a1628c522","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-02T12:38:46Z","title_canon_sha256":"e49d7251f0c297a6cfab737a751e13fc00d695841b71b6bd01cb994450b94ad3"},"schema_version":"1.0","source":{"id":"1507.00548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00548","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00548v2","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00548","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"KAVA7J3XYXMJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KAVA7J3XYXMJRJAR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KAVA7J3X","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:a77610369a3bd5139f265803c54c57617809cea1db80f6fb41c3c10a908e77a2","target":"graph","created_at":"2026-05-18T00:29:02Z","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":"$\\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $\\mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ \\cdots +1+x^2)\\cdot (1+ \\cdots +1 +x^2)^{-1}=1$.","authors_text":"Inge Bethke, Jan A. Bergstra","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-02T12:38:46Z","title":"A negative result on algebraic specifications of the meadow of rational numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00548","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":"sha256:4fc22dcf427c45e67a9e66fe613c088d4003b469c8c11521880037667e4cb655","target":"record","created_at":"2026-05-18T00:29:02Z","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":"f2c9c4e3fb686265717285c06ad87efe65cd2f2f8d0a96fdea7b781a1628c522","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-02T12:38:46Z","title_canon_sha256":"e49d7251f0c297a6cfab737a751e13fc00d695841b71b6bd01cb994450b94ad3"},"schema_version":"1.0","source":{"id":"1507.00548","kind":"arxiv","version":2}},"canonical_sha256":"502a0fa777c5d898a4118c6018d9a7cecc0a533954dd19b4f793e9db395d2718","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"502a0fa777c5d898a4118c6018d9a7cecc0a533954dd19b4f793e9db395d2718","first_computed_at":"2026-05-18T00:29:02.055575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:02.055575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TElEnm8S1tU2v/ZJPAmPjlVhEr4vrzuRklWjPsUVq2wgq+hx3n5EjOgiY7AJE5jXnhCBEGYrTeSfjzvRfgaWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:02.056024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fc22dcf427c45e67a9e66fe613c088d4003b469c8c11521880037667e4cb655","sha256:a77610369a3bd5139f265803c54c57617809cea1db80f6fb41c3c10a908e77a2"],"state_sha256":"c746f9bfd60c97731ba1e4db8a10a8d3c4cbf7fb34c52e3f2f285ffe61f1d317"}