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Using reverse kinematics, we have studied the breakup of 1.0[ital A] GeV gold nuclei incident on a carbon target. The detector system permitted exclusive event reconstruction of nearly all charged reaction products. The moments of the resulting charged fragment distribution provide strong evidence that nuclear matter possesses a critical point observable in finite nuclei. We have determined values for the critical exponents [gamma], [beta], and [tau]. These values are close to those for liquid-gas systems and clearly different than those for 3D percolation and the liquid-gas mean field limit.