The Coefficient Is the Amplitude, Read Backwards: The Price of Starobinsky's R² Inflation

Starobinsky's 1980 paper built the first working inflation model, and the model still stands. This paper does not argue against the model. It prices one step inside it. The model's gravity is f(R) = R + R²/(6M²). The constant M, the scalaron mass, is the R² coefficient in another name. Nothing in the paper derives it. The perturbation amplitude goes in, and M comes out defined by it. At N = 55 the fit gives M/M_Pl = 1.2823×10⁻⁵ and a coefficient 1/(6M²) = 1.0135×10⁹ M_Pl⁻². That is a number near 10⁹ in Planck units, picked by the data and explained by nothing in the paper. The forward check returns the input amplitude exactly, with residuals at floating-point zero, because a dial returns the number it was set to. Independent digits in the amplitude sector: zero. The second dial, N, is set by a reheating history the paper does not compute, and across its standard band the shape slides more than the data's own error bar. Inflation also starts inside one assumed smooth patch, homogeneous and isotropic across 1.5892×10¹⁶ Planck volumes at a fitted scale, with zero derivation equations for that patch in the paper. One real output survives and gets counted at its true size: the N-free shape relation r = 3(1 − n_s)². It derives no dial and no patch. Verdict: a reason was found, and the question remains open (not solved).