{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XN4LVGL7GLXEJJDOVLLBOMMCKB","short_pith_number":"pith:XN4LVGL7","schema_version":"1.0","canonical_sha256":"bb78ba997f32ee44a46eaad6173182507615468b1a212f195bece242023e96e4","source":{"kind":"arxiv","id":"1812.10041","version":2},"attestation_state":"computed","paper":{"title":"An elementary method to compute the algebra generated by some given matrices and its dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RA","authors_text":"J. E. Pascoe","submitted_at":"2018-12-25T05:56:54Z","abstract_excerpt":"We give an efficient solution to the following problem: Given $X_1, \\ldots X_d$ and $Y$ some $n$ by $n$ matrices can we determine if $Y$ is in the unital algebra generated by $X_1, \\ldots, X_d$ as a subalgebra of all $n$ by $n$ matrices? The solution also gives an easy method for computing the dimension of this algebra."},"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":"1812.10041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-25T05:56:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"f058812b45bd47d17898a6b73a530583fcfbb8be55d179d9d0ec17c12afab40c","abstract_canon_sha256":"312b8f794981d8d288499296fd7a9502657536103afb1c6fe1ea5dfc545e1062"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:26.854217Z","signature_b64":"NBmCiIP7yfaUn2ARIUw3qfP6DXRUXd+Nev7oiGv1jmj39t0Xk5drEZSBe/2kxKpl0prxbqpAJG/rMqaBENbNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb78ba997f32ee44a46eaad6173182507615468b1a212f195bece242023e96e4","last_reissued_at":"2026-05-17T23:52:26.853737Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:26.853737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An elementary method to compute the algebra generated by some given matrices and its dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RA","authors_text":"J. E. Pascoe","submitted_at":"2018-12-25T05:56:54Z","abstract_excerpt":"We give an efficient solution to the following problem: Given $X_1, \\ldots X_d$ and $Y$ some $n$ by $n$ matrices can we determine if $Y$ is in the unital algebra generated by $X_1, \\ldots, X_d$ as a subalgebra of all $n$ by $n$ matrices? The solution also gives an easy method for computing the dimension of this algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10041","kind":"arxiv","version":2},"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":"1812.10041","created_at":"2026-05-17T23:52:26.853805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10041v2","created_at":"2026-05-17T23:52:26.853805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10041","created_at":"2026-05-17T23:52:26.853805+00:00"},{"alias_kind":"pith_short_12","alias_value":"XN4LVGL7GLXE","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XN4LVGL7GLXEJJDO","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XN4LVGL7","created_at":"2026-05-18T12:33:01.666342+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/XN4LVGL7GLXEJJDOVLLBOMMCKB","json":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB.json","graph_json":"https://pith.science/api/pith-number/XN4LVGL7GLXEJJDOVLLBOMMCKB/graph.json","events_json":"https://pith.science/api/pith-number/XN4LVGL7GLXEJJDOVLLBOMMCKB/events.json","paper":"https://pith.science/paper/XN4LVGL7"},"agent_actions":{"view_html":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB","download_json":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB.json","view_paper":"https://pith.science/paper/XN4LVGL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10041&json=true","fetch_graph":"https://pith.science/api/pith-number/XN4LVGL7GLXEJJDOVLLBOMMCKB/graph.json","fetch_events":"https://pith.science/api/pith-number/XN4LVGL7GLXEJJDOVLLBOMMCKB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB/action/storage_attestation","attest_author":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB/action/author_attestation","sign_citation":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB/action/citation_signature","submit_replication":"https://pith.science/pith/XN4LVGL7GLXEJJDOVLLBOMMCKB/action/replication_record"}},"created_at":"2026-05-17T23:52:26.853805+00:00","updated_at":"2026-05-17T23:52:26.853805+00:00"}