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We present TeV gamma-ray observations of the Crab Nebula, the standardreference source in ground-based gamma-ray astronomy, using data from the HighAltitude Water Cherenkov (HAWC) Gamma-Ray Observatory. In this analysis we usetwo independent energy-estimation methods that utilize extensive air showervariables such as the core position, shower angle, and shower lateral energydistribution. In contrast, the previously published HAWC energy spectrumroughly estimated the shower energy with only the number of photomultiplierstriggered. This new methodology yields a much improved energy resolution overthe previous analysis and extends HAWC's ability to accurately measuregamma-ray energies well beyond 100 TeV. The energy spectrum of the Crab Nebulais well fit to a log parabola shape $\left(\frac{dN}{dE} = \phi_0\left(E/\textrm{7 TeV}\right)^{-\alpha-\beta\ln\left(E/\textrm{7TeV}\right)}\right)$ with emission up to at least 100 TeV. For the firstestimator, a ground parameter that utilizes fits to the lateral distributionfunction to measure the charge density 40 meters from the shower axis, thebest-fit values are$\phi_o$=(2.35$\pm$0.04$^{+0.20}_{-0.21}$)$\times$10$^{-13}$ (TeV cm$^2$s)$^{-1}$, $\alpha$=2.79$\pm$0.02$^{+0.01}_{-0.03}$, and$\beta$=0.10$\pm$0.01$^{+0.01}_{-0.03}$. For the second estimator, a neuralnetwork which uses the charge distribution in annuli around the core and othervariables, these values are$\phi_o$=(2.31$\pm$0.02$^{+0.32}_{-0.17}$)$\times$10$^{-13}$ (TeV cm$^2$s)$^{-1}$, $\alpha$=2.73$\pm$0.02$^{+0.03}_{-0.02}$, and$\beta$=0.06$\pm$0.01$\pm$0.02. The first set of uncertainties are statistical;the second set are systematic. Both methods yield compatible results. Thesemeasurements are the highest-energy observation of a gamma-ray source to date.

Measurement of the Crab Nebula Spectrum Past 100 TeV with HAWC