{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5GK5BOC2UE2GOJ3C5PTI57735I","short_pith_number":"pith:5GK5BOC2","schema_version":"1.0","canonical_sha256":"e995d0b85aa134672762ebe68efffbea0fd4b923bb744ee67f981bdc86d44d57","source":{"kind":"arxiv","id":"1406.0786","version":1},"attestation_state":"computed","paper":{"title":"Uniformly Presented Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"John D. Wiltshire-Gordon","submitted_at":"2014-06-03T17:04:56Z","abstract_excerpt":"Gaussian elimination answers any question about a finitely presented vector space. However, a \"uniform family\" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only once the number of generators is fixed. We develop a theory of \"uniformly presented vector spaces\" to compute with these uniform families, introducing a formalism of finitely generated functors from the category of finite sets to the category of finite dimensional Q-vector spaces. We show that these representations have finite length and polynomial dimension "},"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":"1406.0786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-03T17:04:56Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"46623a219bc1c0a1c78ede83eb41d32c12b3f47200064f17381f693b398f4eb8","abstract_canon_sha256":"b598ddf42d42acb6b29dad8c00663e2da21f9df8556ea2fc9dfe09016a597a99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:32.827244Z","signature_b64":"K53n6v2zvENXK9TZElIO4ss0AAxNPopuferL9YQIeUG5xW/f5gf2uoNzCvJ7zuOhssNurKdTXVA1QftNwDYsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e995d0b85aa134672762ebe68efffbea0fd4b923bb744ee67f981bdc86d44d57","last_reissued_at":"2026-05-18T02:50:32.826580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:32.826580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformly Presented Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"John D. Wiltshire-Gordon","submitted_at":"2014-06-03T17:04:56Z","abstract_excerpt":"Gaussian elimination answers any question about a finitely presented vector space. However, a \"uniform family\" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only once the number of generators is fixed. We develop a theory of \"uniformly presented vector spaces\" to compute with these uniform families, introducing a formalism of finitely generated functors from the category of finite sets to the category of finite dimensional Q-vector spaces. We show that these representations have finite length and polynomial dimension "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0786","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":"1406.0786","created_at":"2026-05-18T02:50:32.826680+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0786v1","created_at":"2026-05-18T02:50:32.826680+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0786","created_at":"2026-05-18T02:50:32.826680+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GK5BOC2UE2G","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GK5BOC2UE2GOJ3C","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GK5BOC2","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.17371","citing_title":"Representations of categories of finite relational structures and associated endomorphism monoids","ref_index":54,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I","json":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I.json","graph_json":"https://pith.science/api/pith-number/5GK5BOC2UE2GOJ3C5PTI57735I/graph.json","events_json":"https://pith.science/api/pith-number/5GK5BOC2UE2GOJ3C5PTI57735I/events.json","paper":"https://pith.science/paper/5GK5BOC2"},"agent_actions":{"view_html":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I","download_json":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I.json","view_paper":"https://pith.science/paper/5GK5BOC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0786&json=true","fetch_graph":"https://pith.science/api/pith-number/5GK5BOC2UE2GOJ3C5PTI57735I/graph.json","fetch_events":"https://pith.science/api/pith-number/5GK5BOC2UE2GOJ3C5PTI57735I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I/action/storage_attestation","attest_author":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I/action/author_attestation","sign_citation":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I/action/citation_signature","submit_replication":"https://pith.science/pith/5GK5BOC2UE2GOJ3C5PTI57735I/action/replication_record"}},"created_at":"2026-05-18T02:50:32.826680+00:00","updated_at":"2026-05-18T02:50:32.826680+00:00"}