The Kernel Slope Is One: I Smoothed Power-Law Velocity Fields With a Cluster Paper's Own Seeing Kernel, and Its Constant Smoothed Index Fell Out of the Filter Alone

Prices Queue-2 item Q2-14, arXiv:2502.19486 (Fournier et al., XMAGNET velocity structure functions of AGN-driven turbulence in the intracluster medium), on its verified abstract claim, the TSI store record, and the full text. The load-bearing assumed step is the power-law model for the VSF read across the Gaussian seeing kernel (Perseus/SITELLE, FWHM = 0.42 kpc). A Gaussian-smoothed field is infinitely differentiable, so its small-scale VSF index tends to the filter's value 1 for any input. Feeding exact power-law fields (true indices 0.2-0.5) through the paper's own kernel and fitting over its own kernel-scale window (l = 0.4 +/- 0.1 kpc) returns 0.810-0.881 -- mean 0.848 against the paper's printed constant 0.86 +/- 0.06, an input spread of 0.30 compressed to 0.07, Delta-m slope -0.76 against the paper's ~-1, amplitude factor 0.54 against its printed factor of about two; the Appendix D kernel scan is likewise reproduced. The paper's smoothing phenomenology is a property of the filter. DERIVED-INDEPENDENT. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.