{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06427","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.06427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}