The Constant Fitted as an Exponential: Lambda Beside Arrhenius, Priced

The cosmological constant's density is the best-measured unexplained number in physics: fitted by observation to a few percent, and smaller than the Planck density by a factor my bench prints at 8.819236e+122. This paper does not attack that fit, and it does not touch the vacuum problem's headline. It prices the fit's shape — by reading Lambda's number beside the shape my census already priced at the Arrhenius address (CC-127, DOI 10.5281/zenodo.23998529): the fitted exponential. Arrhenius's law spends its whole answer in an exponent, Ea/RT, which two fitted parameters carry; the standard hope for Lambda is the same shape one level up — a density suppressed as the exponential of a large number, rho ~ rho_P exp(−S) — and my bench prices what that shape costs here. On declared fit inputs only (H0 = 67.4 km/s/Mpc and Omega_Lambda = 0.685, both declared and printed as declared wherever spent), the bench returns rho_Lambda = 5.845006e-30 g/cm^3, Lambda = 1.090911e-52 m^-2, and the exponent any exponential mechanism must supply exactly: S = ln(rho_P/rho_Lambda) = 283.092317. The sensitivity is the Arrhenius sensitivity with the volume turned up: the exponent's logarithmic derivative is −1 exactly, so an exponent wrong by 1 percent returns a density wrong by a factor of 1.696111e+01, and an exponent wrong by 0.1 percent returns a density wrong by a factor of 1.327228e+00 — against a fit that observation already holds to percent class. An exponential explanation of Lambda therefore does not explain a small number by a moderate one; it explains a density known to percents by an exponent that must be right to tenths of a percent, 283.092317, derived from nothing fitted. Declared-input discipline is applied to Lambda's number throughout: every cosmological number in this paper is a declared fit input, never a derivation. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — a pricing of the fit's shape, explicitly not a solution claim and not a falsification of the fitted value, which is the best-attested number in this paper. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.