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When $t=2$ the resulting quotient ring $K[X]/\\mathfrak P_2$ is a normal complete intersection domain. When $t>2$ we break the problem into cases depending on a fixed rank, $r$, of $X$. We show when $r=n$ for any $t$, the respective images of $\\mathfrak P_t$ and $\\mathfrak P_{n-t}$ in the lo"},"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":"1410.1910","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-07T20:59:51Z","cross_cats_sorted":[],"title_canon_sha256":"247c4bdd158ca4e0fee1461fbe9317959bcfc6380192a3247a93afd5fe5a54e0","abstract_canon_sha256":"493795d74272ed75a78020aec2bea38bcbf0bb2ce4a75fe4a10c0b1aa4898e11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:01.846176Z","signature_b64":"FuB/Fm6qqOmCPtrqE1GnzYc3F08QP/oPve128pwHg5KRt9GeZS8wBzGUeLI8bBTKRfY3+j3nSmjgYHzbxqIoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a41ba90a2dc2e5d1ade90420ac173af051643778a82a307a53cf0ff09639dd04","last_reissued_at":"2026-05-18T01:36:01.845719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:01.845719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideals Generated by Principal Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ashley K. Wheeler","submitted_at":"2014-10-07T20:59:51Z","abstract_excerpt":"A minor is principal means it is defined by the same row and column indices. Let $X$ be a square generic matrix, $K[X]$ the polynomial ring in entries of $X$, over an algebraically closed field, $K$. For fixed $t\\leq n$, let $\\mathfrak P_t$ denote the ideal generated by the size $t$ principal minors of $X$. When $t=2$ the resulting quotient ring $K[X]/\\mathfrak P_2$ is a normal complete intersection domain. When $t>2$ we break the problem into cases depending on a fixed rank, $r$, of $X$. We show when $r=n$ for any $t$, the respective images of $\\mathfrak P_t$ and $\\mathfrak P_{n-t}$ in the lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1910","kind":"arxiv","version":3},"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":"1410.1910","created_at":"2026-05-18T01:36:01.845777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.1910v3","created_at":"2026-05-18T01:36:01.845777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1910","created_at":"2026-05-18T01:36:01.845777+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQN2SCRNYLS5","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQN2SCRNYLS5DLPJ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQN2SCRN","created_at":"2026-05-18T12:28:52.271510+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/UQN2SCRNYLS5DLPJAQQKYFZ26B","json":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B.json","graph_json":"https://pith.science/api/pith-number/UQN2SCRNYLS5DLPJAQQKYFZ26B/graph.json","events_json":"https://pith.science/api/pith-number/UQN2SCRNYLS5DLPJAQQKYFZ26B/events.json","paper":"https://pith.science/paper/UQN2SCRN"},"agent_actions":{"view_html":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B","download_json":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B.json","view_paper":"https://pith.science/paper/UQN2SCRN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.1910&json=true","fetch_graph":"https://pith.science/api/pith-number/UQN2SCRNYLS5DLPJAQQKYFZ26B/graph.json","fetch_events":"https://pith.science/api/pith-number/UQN2SCRNYLS5DLPJAQQKYFZ26B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B/action/storage_attestation","attest_author":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B/action/author_attestation","sign_citation":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B/action/citation_signature","submit_replication":"https://pith.science/pith/UQN2SCRNYLS5DLPJAQQKYFZ26B/action/replication_record"}},"created_at":"2026-05-18T01:36:01.845777+00:00","updated_at":"2026-05-18T01:36:01.845777+00:00"}