Site Specific Knight Shift Measurements of the Dilute Kondo lattice System Ce$_{1-x}$La$_x$CoIn$_5$.

$^{115}$In Nuclear magnetic resonance data are presented for a series of Ce$_{1-x}$La$_x$CoIn$_5$ crystals with different La dilutions, $x$. Multiple In(1) sites associated with different numbers of nearest-neighbor cerium atoms exhibit different Knight shifts and spin lattice relaxation rates. Analysis of the temperature dependence of these sites reveals both an evolution of the heavy electron coherence as a function of dilution, as well as spatial inhomogeneity associated with a complete suppression of antiferromagnetic fluctuations in the vicinity of the La sites. Quantum critical fluctuations persist within disconnected Ce clusters with dilution levels up to 75%, despite the fact that specific heat shows Fermi liquid behavior in dilute samples.