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Tensor exponents are fundamental from the standpoint of algorithms and computational complexity theory; for example, the exponent $\\omega$ of matrix multiplication can be characterized as $\\omega=2\\sigma(\\mathrm{MM}_2)$, where $\\mathrm{MM}_2\\in\\mathbb{F}^4\\otimes\\mathbb{F}^4\\otimes\\mathbb{F}^4$ is the tensor that represents $2\\times 2$ matrix multiplication.\n  Our main result is"},"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":"2404.06427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2024-04-09T16:18:13Z","cross_cats_sorted":["cs.DS","math.AG"],"title_canon_sha256":"7ac33d2b77f1d64cc3568064de5d4d559f5b4d5dd7ab5674796e48230a08d0c3","abstract_canon_sha256":"60ac756af67d3b2f564c23d859d6ce6d1f33fcab916054a6c3a42a0c0bb592f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:08.921189Z","signature_b64":"swsszmyeAC6BLRbF1n9J+W9XslRLXEmFmOcVBU5IlHCt//QEyepJxKKDZEqM67Ej8UswrD6viaEZUix1T0E7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff7d7c71e2720aadd99f8b0b083d781a2025cdb893a5042d758ba54949e901f","last_reissued_at":"2026-07-05T08:06:08.920778Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:08.920778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A universal sequence of tensors for the asymptotic rank conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.AG"],"primary_cat":"cs.CC","authors_text":"Mateusz Micha{\\l}ek, Petteri Kaski","submitted_at":"2024-04-09T16:18:13Z","abstract_excerpt":"The exponent $\\sigma(T)$ of a tensor $T\\in\\mathbb{F}^d\\otimes\\mathbb{F}^d\\otimes\\mathbb{F}^d$ over a field $\\mathbb{F}$ captures the base of the exponential growth rate of the tensor rank of $T$ under Kronecker powers. 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