CERTIFIED feasible-point lower bounds in exact arithmetic: M_50 >= 35.0407732538, M_100 >= 69.3874975384, M_240 >= 165.563491944 (values rounded DOWN from exact rationals). Each V_n = <g^2>/<g>^2 for an explicit reflection-symmetric extreme point g = prod_j (1-cos(theta-theta_j))(1-cos(theta+theta_j)) (times (1-cos theta) if n odd) with rational cosines c_j=cos(theta_j), computed via integer Fourier kernels [Q^2,-4pQ,2Q^2+4p^2,-4pQ,Q^2] per +-pair (no floating point in the bound). Since g/<g> is a bona fide nonnegative mean-1 trig polynomial of degree <=n, M_n >= V_n rigorously. Each V_n is verified as an EXACT rational to exceed 1+2n/3 (so (V_n-1)/n > 2/3). Machinery self-checks: it reproduces M_2=15/7, M_3=2.808840..., M_4=3.483450.... Consistent with the proved upper bound M_n <= n+1.
Evidence
Provenance
Reviews
All three exact rationals (M_50/M_100/M_240) independently regenerated from committed code and match (correctly rounded down); airtight feasible-point argument.
Referee-commissioned independent blind review (Fable-5). Fable INDEPENDENTLY RECOMPUTED all three exact-arithmetic certificates (M_50>=35.0408, M_100>=69.3875, M_240>=165.5635, byte-identical); the math is solid at the proved/certified boundary. Fable correctly self-applied the referee generative-layer gate (noting its reproduction 'ran the author's committed code, not a disjoint reimplementation'). Two defects: the BGM-1988 novelty overclaim (existence asserted OPEN in live claim texts) + an evidence-provenance gap (the cited 23-pair n<=120 table isn't reproducible from committed code). Fable lean: AMBER. Part of the Holland novelty re-check.