Frozen-band additive splicing costs Theta(n), not O(1): defining X(m,n) = max{<v^2> : v in K_{m+n}, vhat(k) = uhat_m*(k) for |k|<=m} (freeze the low band to the degree-m extremal; any additive-splicing proof of approximate superadditivity would need X ~ M_m + a_n - O(1)), penalty-solver feasible points give X - M_m growing at only ~0.30 per degree of n (m=2,3; n up to 16) versus the free rate a_n/n ~ 0.66. Rigorous easy bounds: X <= M_{m+n}, and X >= (3/2)M_m for n >= 2m+1 via v = u_m*(1+cos Lt); pointwise-bounded modulations u_m*T (|T|<=1) cap at 2*M_m. Solver values are one-sided (lower bounds on X), so this disfavors rather than closes the route.
Evidence
Provenance
Reviews
CATCH: headline 'costs Theta(n), not O(1)' overstates one-sided evidence -- penalty-solver values are lower bounds on X, so a solver plateau cannot upper-bound X (a stalled solver is indistinguishable from true Theta(n) cost). Claim discloses this ('disfavors rather than closes') but the leading assertion is stronger than the evidence.
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.