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Further insisting that $\\det_2(AB)=\\det_2(A)\\det_2(B)$, for Kronecker products $A$ and $B$, yields a multiplicative monoid of matrices. This leads to a determinant-root operation $\\text{Det}$ which satisfies $\\text{Det}(\\text{Det}_2(A)) = \\text{Det}(A)$ when $A$ is a Kronecker product of matrices for which $\\text{Det}$ is defined."},"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":"1709.10253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T06:54:12Z","cross_cats_sorted":[],"title_canon_sha256":"0370d183396db2e6837bf52f9a5c4719024b1486422e7fca77115b3d40415c84","abstract_canon_sha256":"2b69fe4cfef29c5dc98e25607d0648f3d62d22d46f3aa54bf19813b9399de523"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:12.587431Z","signature_b64":"IRSS6NOCakUfoEVAen3fenCRPNKUKzlHoPHO4bzvNeGwarPbOR2OUT9PoJSpBlm1OHisvmiKaqcVce+fiE/LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27185f3db9aa66d5a71ce8702d207d481af56679c1736f93a3804188bf7d6b60","last_reissued_at":"2026-05-18T00:26:12.586990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:12.586990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial determinants of Kronecker products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yorick Hardy","submitted_at":"2017-09-29T06:54:12Z","abstract_excerpt":"Let $\\det_2(A)$ be the block-wise determinant (partial determinant). 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This leads to a determinant-root operation $\\text{Det}$ which satisfies $\\text{Det}(\\text{Det}_2(A)) = \\text{Det}(A)$ when $A$ is a Kronecker product of matrices for which $\\text{Det}$ is defined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10253","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":"1709.10253","created_at":"2026-05-18T00:26:12.587061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.10253v2","created_at":"2026-05-18T00:26:12.587061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10253","created_at":"2026-05-18T00:26:12.587061+00:00"},{"alias_kind":"pith_short_12","alias_value":"E4MF6PNZVJTN","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"E4MF6PNZVJTNLJY4","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"E4MF6PNZ","created_at":"2026-05-18T12:31:12.930513+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/E4MF6PNZVJTNLJY45BYC2ID5JA","json":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA.json","graph_json":"https://pith.science/api/pith-number/E4MF6PNZVJTNLJY45BYC2ID5JA/graph.json","events_json":"https://pith.science/api/pith-number/E4MF6PNZVJTNLJY45BYC2ID5JA/events.json","paper":"https://pith.science/paper/E4MF6PNZ"},"agent_actions":{"view_html":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA","download_json":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA.json","view_paper":"https://pith.science/paper/E4MF6PNZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.10253&json=true","fetch_graph":"https://pith.science/api/pith-number/E4MF6PNZVJTNLJY45BYC2ID5JA/graph.json","fetch_events":"https://pith.science/api/pith-number/E4MF6PNZVJTNLJY45BYC2ID5JA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA/action/storage_attestation","attest_author":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA/action/author_attestation","sign_citation":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA/action/citation_signature","submit_replication":"https://pith.science/pith/E4MF6PNZVJTNLJY45BYC2ID5JA/action/replication_record"}},"created_at":"2026-05-18T00:26:12.587061+00:00","updated_at":"2026-05-18T00:26:12.587061+00:00"}