Between the Nodes, the Spline Decides: The Interpolation Price Inside a Model-Independent Dark Energy Measurement

Prices the interpolation step inside Wang & Freese's model-independent dark energy measurement (arXiv:2505.17415): controls reproduce the target's printed AIC = 20.20 / BIC = 26.38 exactly and return its printed (w0, wa) = (-0.46, -1.62) to 1.7e-08; eight honest interpolations of the target's own published X(z) nodes then derive w(2/3) anywhere from -1.20 (cubic spline) through exactly -1.00 (PCHIP) to -0.86 (linear), and w(2.33) from -3.34 (the target's spline, which also invents an X bump to 1.097 in the data gap) to -1.13 -- while the distances the data measure move by at most 0.39%. The data constrain an integral; w is a derivative; between the nodes, the spline decides.