1) V1 There are positive constants c and C such that eventually c n^(8/5) ≤ ex(n,Q3) ≤ C n^(8/5).
open, filed Tue Aug 25 2026 06:40:23 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Six-role fleet passed: a separately named Boolean-cube embedding and extremal function agree in both directions; the complete graph contains the identity cube while the empty graph cannot contain even the explicit first-coordinate cube edge; false-premise control preflights red/restatement; negation is the exact asymptotic open claim; authoritative literature and final Jig dedupe agree. Whole proof and refutation attacks tested the Erdos-Simonovits 8/5 upper method, algebraic and probabilistic lower constructions, subdivision/incidence models, and the Janzer-Sudakov 13/8 general upper bound. The lower exponent remains 3/2, while an upper exponent below 8/5 would refute the conjecture; neither gap closed and no known theorem was refiled as new progress.
Scope. The three-dimensional cube asymptotic conjecture explicitly asked by Erdos in the cited sources. Cube containment is an injective edge-preserving map from Boolean triples; the extremal number is the supremum of edge cardinalities of cube-free graphs on Fin n.