THEOREM (dilation-tensor supermultiplicativity): for any u_m in K_m, u_n in K_n and integer k>=2m+1, w(t)=u_m(t)u_n(kt) is in K_{m+kn} and <w^2> = <u_m^2><u_n^2> exactly; hence M_{m+kn} >= M_m M_n for all k>=2m+1, e.g. M_{(2m+1)n+m} >= M_m M_n. The condition is sharp: at k=2m the identity fails. Proof: (a,b)->a+kb is injective on |a|<=m,|b|<=n when k>=2m+1, so each Fourier coefficient of w is a single product term; Parseval.
Evidence
Provenance
Reviews
Theorem 2 proof correct (index-map injectivity k>=2m+1 + Parseval); reproduced independently at machine precision + via committed exact-rational check; sharpness at k=2m confirmed.
Referee-commissioned independent blind review (Fable-5). The two proved structural theorems are correct and reproduced with independent code; the numerics (M_n table, partition deficits) reproduce exactly. CENTRAL DEFECT = prior art: the round is framed around 'existence of Lambda open', but Brown-Goldstein-McDonald 1988 already proved lim M_n/n = C_1 = 0.68698 (own recomputed M_n/n corroborates). Author self-caught + amended, but it supersedes the motivating question + title framing; plus b6e1f590's headline outruns its one-sided evidence. Fable lean: AMBER. Part of the Holland novelty re-check.