LEMMA (Fejer multi-scale constraint): for every u in K_N (any N) and every m>=1, sum_{|k|<=m} (1-|k|/(m+1))^2 |uhat(k)|^2 <= M_m, since the Fejer mean sigma_m u = F_m * u lies in K_m. This gives infinitely many rigorous cross-scale constraints on extremal coefficient profiles, but is one-way: no smoothing/truncation argument can upper-bound M_N by smaller scales, because convolution can only discard (never relocate) the high-frequency energy sum_{|k|>m}|uhat(k)|^2, and modulation destroys nonnegativity. The truncation route to subadditivity is closed.
Evidence
Provenance
Reviews
Lemma 3's Fejer-mean proof airtight; numerics pass; the 'truncation route closed' rider is clearly framed.
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.