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We analyze {\it simultaneously} six composite {\it RXTE} spectra of GX 339--4in the hard state comprising 77 million counts collected over 196 ks. Thesource spectra are ordered by luminosity and spanthe range 1.6\% to 17\% of theEddington luminosity. Crucially, using our new tool {\tt pcacorr}, were-calibrate the data to a precision of 0.1\%, an order of magnitudeimprovement over all earlier work. Using our advanced reflection model {\ttrelxill}, we target the strong features in the component of emission reflectedfrom the disk, namely, the relativistically-broadened Fe K emission line, theFe K edge and the Compton hump. We report results for two joint fits to the sixspectra: For the first fit, we fix the spin parameter to its maximal value($a_*=0.998$) and allow the inner disk radius $R_{\rm in}$ to vary. Resultsinclude (i) precise measurements of $R_{\rm in}$, with evidence that the diskbecomes slightly truncated at a few percent of Eddington; and (ii) anorder-of-magnitude swing with luminosity in the high energy cutoff, whichreaches $>890$ keV at our lowest luminosity. For the second fit, we make thestandard assumption in estimating spin that the inner edge of the accretiondisk is located at the innermost stable circular orbit ($R_\mathrm{in} =R_\mathrm{ISCO}$) and find $a_* = 0.95^{+0.03}_{-0.05}$ (90\% confidence,statistical). For both fits, and at the same level of statistical confidence,we estimate that the disk inclination is $i = 48\pm 1$ deg and that the Feabundance is super-solar, $A_\mathrm{Fe} = 5\pm1$.

X-ray Reflection Spectroscopy of the Black Hole GX 339-4: Exploring the Hard State with Unprecedented Sensitivity