{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SQZYHQXNGLWN7CEXQQ7CAUQFS7","short_pith_number":"pith:SQZYHQXN","schema_version":"1.0","canonical_sha256":"943383c2ed32ecdf8897843e20520597fe9b8833eb5d5a7680d1cd3c85ae4199","source":{"kind":"arxiv","id":"1508.00690","version":2},"attestation_state":"computed","paper":{"title":"Non-commutative Edmonds' problem and matrix semi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"cs.DS","authors_text":"G\\'abor Ivanyos, K. V. Subrahmanyam, Youming Qiao","submitted_at":"2015-08-04T07:39:16Z","abstract_excerpt":"In 1967, Edmonds introduced the problem of computing the rank over the rational function field of an $n\\times n$ matrix $T$ with integral homogeneous linear polynomials. In this paper, we consider the non-commutative version of Edmonds' problem: compute the rank of $T$ over the free skew field. It is known that this problem relates to the ring of matrix semi-invariants. In particular, if the nullcone of matrix semi-invariants is defined by elements of degree $\\leq \\sigma$, then there follows a $\\mathrm{poly}(n, \\sigma)$-time randomized algorithm to decide whether the non-commutative rank of $T"},"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":"1508.00690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-08-04T07:39:16Z","cross_cats_sorted":["cs.CC","math.AC","math.RA"],"title_canon_sha256":"1184576726eaba362152f55a63d3858188d4c618a12fde2cac1ff367d437d198","abstract_canon_sha256":"da8212d28a7914d362ea7258d24a0ec0cb0063d97d3376ef07a79fdcdec39e1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:20.008255Z","signature_b64":"12W488d47mSv3MJu69RQlpfObNK8Qsno2UTPloEaqCfzRDybN2QFj6A3+arrNYk/LC+nFXUp3ItWOt1opxLpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943383c2ed32ecdf8897843e20520597fe9b8833eb5d5a7680d1cd3c85ae4199","last_reissued_at":"2026-05-18T01:12:20.007927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:20.007927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative Edmonds' problem and matrix semi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"cs.DS","authors_text":"G\\'abor Ivanyos, K. V. Subrahmanyam, Youming Qiao","submitted_at":"2015-08-04T07:39:16Z","abstract_excerpt":"In 1967, Edmonds introduced the problem of computing the rank over the rational function field of an $n\\times n$ matrix $T$ with integral homogeneous linear polynomials. In this paper, we consider the non-commutative version of Edmonds' problem: compute the rank of $T$ over the free skew field. It is known that this problem relates to the ring of matrix semi-invariants. In particular, if the nullcone of matrix semi-invariants is defined by elements of degree $\\leq \\sigma$, then there follows a $\\mathrm{poly}(n, \\sigma)$-time randomized algorithm to decide whether the non-commutative rank of $T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00690","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":"1508.00690","created_at":"2026-05-18T01:12:20.007977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.00690v2","created_at":"2026-05-18T01:12:20.007977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00690","created_at":"2026-05-18T01:12:20.007977+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQZYHQXNGLWN","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQZYHQXNGLWN7CEX","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQZYHQXN","created_at":"2026-05-18T12:29:42.218222+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/SQZYHQXNGLWN7CEXQQ7CAUQFS7","json":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7.json","graph_json":"https://pith.science/api/pith-number/SQZYHQXNGLWN7CEXQQ7CAUQFS7/graph.json","events_json":"https://pith.science/api/pith-number/SQZYHQXNGLWN7CEXQQ7CAUQFS7/events.json","paper":"https://pith.science/paper/SQZYHQXN"},"agent_actions":{"view_html":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7","download_json":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7.json","view_paper":"https://pith.science/paper/SQZYHQXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.00690&json=true","fetch_graph":"https://pith.science/api/pith-number/SQZYHQXNGLWN7CEXQQ7CAUQFS7/graph.json","fetch_events":"https://pith.science/api/pith-number/SQZYHQXNGLWN7CEXQQ7CAUQFS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7/action/storage_attestation","attest_author":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7/action/author_attestation","sign_citation":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7/action/citation_signature","submit_replication":"https://pith.science/pith/SQZYHQXNGLWN7CEXQQ7CAUQFS7/action/replication_record"}},"created_at":"2026-05-18T01:12:20.007977+00:00","updated_at":"2026-05-18T01:12:20.007977+00:00"}