The Alpha Paradox: A Metrological Map of AGL-EFT Identiability in the SPARC Rotation Curve Sample Paper IV of the AGL Programme

We present a systematic metrological analysis of the Adiabatic Geometric Leveling eec-tive eld theory (AGL-EFT) applied to 21 priority galaxies from the SPARC catalog, selectedby the identiability criterion α ∈ [Rmin, Rmax] and strong model evidence (∆AIC < −6).Using real SPARC rotmod les and a matched-lter reparametrization (β0, β1) with the darkmatter halo held xed (eliminating the circularity identied in Paper III), we nd: (i) theamplitude β0 = Λobs is detected at |SNR| > 3 in 12/21 galaxies (57%); (ii) the radial slopeβ1 = Λ/(2α) is detected in 13/21 galaxies (62%); (iii) the inferred range scale αinf = β0/(2β1)has a median of 15.9 kpc with IQR [11.2, 18.9] kpc, strikingly narrower than the chi-squaredbest-t values (αfit median 2.8 kpc, IQR [0.8, 9.6] kpc). This discrepancy the Alpha Para-dox reveals that the traditional four-parameter chi-squared t converges to a spuriouslocal minimum with small α, while the halo-xed matched lter recovers a physically con-sistent range scale near 15 kpc. The amplitude β0 is consistent with zero mean (Wilcoxonp = 0.30) across the 16-galaxy partial regime, conrming the AGL prediction of system-to-system variation without universal bias. These results establish the metrological foundationfor Paper V, which will extend the analysis to the full SPARC and LITTLE THINGS samplesusing the identiability criterion as the primary selection lter.