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Let $\\rho$ be the Hurwitz-Radon function defined as $\\rho(n)=2^b+8c$ for nonnegative integers $a,b,c$ such that $n=(2a+1)2^{b+4c}$ and $0\\leq b<4$. If $m \\leq \\rho(n)$, then the set of $m\\times n\\times (m-1)n$ tensors has two typical ranks $(m-1)n,(m-1)n+1$. In this paper, we show that the converse is also true: if $m > \\rho(n)$, then the set of $m\\times n\\times (m-1)n$ tensors has onl"},"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":"1210.6713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-10-25T01:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"300cb43a86c611fdf34f14d7123853a499a14b64b3371d1ae41508c0724a5a1f","abstract_canon_sha256":"9b3a56170f4bbba88e8d4905cd9cbeb8b73bc279dd23536ab9a5022dbc108d00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:23.310477Z","signature_b64":"Qj/Q2K3bYVbp6ucRujcEzkD5o4j6mUWWopm14Qc5Kg80nTUnoAhtKPmU1NxD8G055+C8NXQ6HXyKnZ8CqsmqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcd9a1c2a9322e3449a720f58dec937b2c35998c617a39f16b35aab22c9ad905","last_reissued_at":"2026-05-18T03:42:23.309900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:23.309900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Typical rank of $m\\times n\\times (m-1)n$ tensors with $3\\leq m\\leq n$ over the real number field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mitsuhiro Miyazaki, Toshio Sakata, Toshio Sumi","submitted_at":"2012-10-25T01:15:37Z","abstract_excerpt":"Tensor type data are used recently in various application fields, and then a typical rank is important. 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