Laplace — the map's dynamics (decay/growth), beyond the steady spectrum

Matt: 'laplace transform ... missing.' Fourier gives the STEADY spectrum (the imaginary axis); Laplace adds the REAL axis s=sigma+i*omega — decay/growth RATES. The map's eigenvalue spectrum decays EXPONENTIALLY, which is the Laplace domain: each mode descends from the source/fundamental at a fixed rate. The 'rate of descent from source' made literal; Laplace is the transform for the DYNAMICS (how the arrangement responds, decays, settles), where Fourier is the snapshot. HONEST STATUS: plausible — intuition proposes, the assay disposes; this is the operator's seed, not a verified result. Caveat: A lens, plausible: the exponential fit is REAL (R^2=0.995), but 'the map is a Laplace/linear-relaxation system' is provisional; what the decay rate MEANS for correctness is open. Tie to the tune-criterion: does cleaner/faster relaxation track a more in-tune (more correct) arrangement?