  We present JWST observations of the Crab Nebula, the iconic remnant of the
historical SN 1054. The observations include NIRCam and MIRI imaging mosaics,
plus MIRI/MRS IFU spectra that probe two select locations within the ejecta
filaments. We derive a high-resolution map of dust emission and show that the
grains are concentrated in the innermost, high-density filaments. These dense
filaments coincide with multiple synchrotron bays around the periphery of the
Crab's pulsar wind nebula (PWN). We measure synchrotron spectral index changes
in small-scale features within the PWN's torus region, including the well-known
knot and wisp structures. The index variations are consistent with Doppler
boosting of emission from particles with a broken power-law distribution,
providing the first direct evidence that the curvature in the particle
injection spectrum is tied to the acceleration mechanism at the termination
shock. We detect multiple nickel and iron lines in the ejecta filaments and use
photoionization models to derive nickel-to-iron abundance ratios that are a
factor of 3-8 higher than the solar ratio. We also find that the previously
reported order-of-magnitude higher Ni/Fe values from optical data are
consistent with the lower values from JWST when we reanalyze the optical
emission using updated atomic data and account for local extinction from dust.
We discuss the implications of our results for understanding the nature of the
explosion that produced the Crab Nebula and conclude that the observational
properties are most consistent with a low-mass iron-core-collapse supernova,
even though an electron-capture explosion cannot be ruled out.
