{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UJ3KDJGCV7MAJOPZCGMEAOULI5","short_pith_number":"pith:UJ3KDJGC","schema_version":"1.0","canonical_sha256":"a276a1a4c2afd804b9f91198403a8b476038d587c6f6b63752b341707775f95b","source":{"kind":"arxiv","id":"1812.08205","version":1},"attestation_state":"computed","paper":{"title":"On polynomials that are not quite an identity on an associative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Riley, Eric Jespers, Mayada Shahada","submitted_at":"2018-12-19T19:25:27Z","abstract_excerpt":"Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by $\\S_A(f)$, $\\A_A(f)$ and $\\I_A(f)$, respectively, the `verbal' subspace, subalgebra, and ideal, in $A$, generated by the set of all $f$-values in $A$. We begin by studying the following problem: if $\\S_A(f)$ is finite-dimensional, is it true that $\\A_A(f)$ and $\\I_A(f)$ are also finite-dimensional? We then consider the dual to this problem for `marginal' subspaces that are finite-codimensional in $A$. If $f$ is multilinear, the marginal subspace, $\\widehat{\\S}_A(f)$, of $f$ in $A$ is the se"},"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":"1812.08205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-19T19:25:27Z","cross_cats_sorted":[],"title_canon_sha256":"e905c6b29723c254a8c74f79e0270f7baed74b1fc80e1d3c6f9753af2d52f3a9","abstract_canon_sha256":"e0a75e1cfb5c22ba21075c4ec32ec99f055ecd6a9648c69acdf0608a6d34bf09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:51.952692Z","signature_b64":"oJsJv5xnhUxSmvzHhnSbZ3cMy6olx8HsgOOTm7LURilskPJx9p2RCuMJZWaDhPQ2d2TxpW6tt0hm0W5zq0k1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a276a1a4c2afd804b9f91198403a8b476038d587c6f6b63752b341707775f95b","last_reissued_at":"2026-05-17T23:57:51.952052Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:51.952052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On polynomials that are not quite an identity on an associative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Riley, Eric Jespers, Mayada Shahada","submitted_at":"2018-12-19T19:25:27Z","abstract_excerpt":"Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by $\\S_A(f)$, $\\A_A(f)$ and $\\I_A(f)$, respectively, the `verbal' subspace, subalgebra, and ideal, in $A$, generated by the set of all $f$-values in $A$. We begin by studying the following problem: if $\\S_A(f)$ is finite-dimensional, is it true that $\\A_A(f)$ and $\\I_A(f)$ are also finite-dimensional? We then consider the dual to this problem for `marginal' subspaces that are finite-codimensional in $A$. If $f$ is multilinear, the marginal subspace, $\\widehat{\\S}_A(f)$, of $f$ in $A$ is the se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08205","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":"1812.08205","created_at":"2026-05-17T23:57:51.952154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08205v1","created_at":"2026-05-17T23:57:51.952154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08205","created_at":"2026-05-17T23:57:51.952154+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJ3KDJGCV7MA","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJ3KDJGCV7MAJOPZ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJ3KDJGC","created_at":"2026-05-18T12:32:56.356000+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/UJ3KDJGCV7MAJOPZCGMEAOULI5","json":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5.json","graph_json":"https://pith.science/api/pith-number/UJ3KDJGCV7MAJOPZCGMEAOULI5/graph.json","events_json":"https://pith.science/api/pith-number/UJ3KDJGCV7MAJOPZCGMEAOULI5/events.json","paper":"https://pith.science/paper/UJ3KDJGC"},"agent_actions":{"view_html":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5","download_json":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5.json","view_paper":"https://pith.science/paper/UJ3KDJGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08205&json=true","fetch_graph":"https://pith.science/api/pith-number/UJ3KDJGCV7MAJOPZCGMEAOULI5/graph.json","fetch_events":"https://pith.science/api/pith-number/UJ3KDJGCV7MAJOPZCGMEAOULI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5/action/storage_attestation","attest_author":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5/action/author_attestation","sign_citation":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5/action/citation_signature","submit_replication":"https://pith.science/pith/UJ3KDJGCV7MAJOPZCGMEAOULI5/action/replication_record"}},"created_at":"2026-05-17T23:57:51.952154+00:00","updated_at":"2026-05-17T23:57:51.952154+00:00"}