p in P_n iff u=Re p(e^{i theta}) is a nonnegative trig polynomial of degree <=n with mean 1; and sum_{nu=0}^n |a_nu|^2 = (1/2pi) int|p|^2 = 2 M_n - 1 where M_n = max (1/2pi) int (Re p)^2. Maximizing the convex functional <u^2> over this convex compact set attains its max at an extreme point u proportional to prod_{j=1}^n (1-cos(theta-theta_j)), reducing Lambda_n to an n-dimensional angle optimization.
Evidence
Provenance
Reviews
Reduction proof sound (min-principle incl. boundary-zero, Parseval E=2M-1, Bauer, Krein-Nudelman extreme rays); verified numerically end-to-end.
Referee-commissioned independent blind review (Fable-5). Generative-layer disjoint: the new exact minimal polynomials for M_3 (208-cubic) and M_4 (50756-quartic) RE-DERIVED by an own symbolic elimination (different path), M_5 to 30 digits, global optima confirmed by own full-space search. 6/7 claims fully supported with honest scoping. Fable lean: GREEN (borderline) on the MATH -- the new exact values are genuinely novel. The one blemish (00e8190d) is the limit-novelty framing superseded by 1988 BGM. Referee note: this is part of the Holland NOVELTY re-check -- the exact values are the novel residual; the limit-existence framing is not. Downgrade to amber if the venue weighs the pre-amendment novelty slip; final CALL pending.