{"paper":{"title":"Complete Existence Classification of Seven-Partite Absolutely Maximally Entangled States","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Fei Shi, Lvzhou Li, Qi Zhao, Xiande Zhang","submitted_at":"2026-08-02T05:26:34Z","abstract_excerpt":"We prove that an absolutely maximally entangled state of seven qudits exists if and only if the local dimension satisfies $d\\geq 3$. Prior to this work, to the best of our knowledge, $\\text{AME}(7,d)$ states were known to exist only when $d$ is a prime power other than $2$, or when $d$ can be expressed as a product of dimensions for which existence was already known. Since it has been proved that no $\\text{AME}(7,2)$ state exists, it remains to establish existence for all $d\\geq 3$. We construct cyclic quadratic-phase states for every odd local dimension and develop a coupled binary--odd-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01011","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/2608.01011/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"}