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We prove that given two terms that are separated in any algebra, there exists a finite algebra in which they are separated. As a corollary, we obtain that whenever the sentence $\\sigma$ is a universally quantified conjunction of negated atomic formulas, $\\sigma$ is consistent iff"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.04911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-19T13:16:18Z","cross_cats_sorted":[],"title_canon_sha256":"62a943cd8b19add6a59e8043118c5c659d90792a767e4146e71a153fe3ec69c5","abstract_canon_sha256":"d15470315ca4e6735f8c811c216e3b4c18f9a5a6823f0b91abdbc2641a9d9fa4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:31.561722Z","signature_b64":"XnBIA1M9jhMnnKWmT6HzTpdgciH7JkTmTTTf/gNEzuAn2D54bAbskD03wjinw92GHft9JV1V71VU9ALw4JchCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c3dc6495c6674d158285d52fbcbef9bb73adf53167cb9a9766035c1bda76f85","last_reissued_at":"2026-05-18T01:22:31.561122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:31.561122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Term inequalities in finite algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Hobby","submitted_at":"2016-01-19T13:16:18Z","abstract_excerpt":"Given an algebra $\\mathbf{A}$, and terms $s(x_{1},x_{2},\\dots x_{k})$ and $t(x_{1},x_{2},\\dots x_{k})$ of the language of ${\\mathbf A}$, we say that $s$ and $t$ are {\\em separated} in ${\\mathbf A}$ iff for all $a_{1},a_{2}\\dots a_{k}\\in A$, $s(a_{1},a_{2},\\dots a_{k})$ and $t(a_{1},a_{2},\\dots a_{k})$ are never equal. We prove that given two terms that are separated in any algebra, there exists a finite algebra in which they are separated. As a corollary, we obtain that whenever the sentence $\\sigma$ is a universally quantified conjunction of negated atomic formulas, $\\sigma$ is consistent iff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04911","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.04911","created_at":"2026-05-18T01:22:31.561206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.04911v1","created_at":"2026-05-18T01:22:31.561206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04911","created_at":"2026-05-18T01:22:31.561206+00:00"},{"alias_kind":"pith_short_12","alias_value":"LQ64MSK4MZ2N","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LQ64MSK4MZ2NCWBI","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LQ64MSK4","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO","json":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO.json","graph_json":"https://pith.science/api/pith-number/LQ64MSK4MZ2NCWBILVJPXS7PTO/graph.json","events_json":"https://pith.science/api/pith-number/LQ64MSK4MZ2NCWBILVJPXS7PTO/events.json","paper":"https://pith.science/paper/LQ64MSK4"},"agent_actions":{"view_html":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO","download_json":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO.json","view_paper":"https://pith.science/paper/LQ64MSK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.04911&json=true","fetch_graph":"https://pith.science/api/pith-number/LQ64MSK4MZ2NCWBILVJPXS7PTO/graph.json","fetch_events":"https://pith.science/api/pith-number/LQ64MSK4MZ2NCWBILVJPXS7PTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO/action/storage_attestation","attest_author":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO/action/author_attestation","sign_citation":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO/action/citation_signature","submit_replication":"https://pith.science/pith/LQ64MSK4MZ2NCWBILVJPXS7PTO/action/replication_record"}},"created_at":"2026-05-18T01:22:31.561206+00:00","updated_at":"2026-05-18T01:22:31.561206+00:00"}