We report the observation of electroweak single top quark production in 3.2 fb-1 of p anti-p collision data collected by the Collider Detector at Fermilab at s**(1/2) = 1.96 TeV. Candidate events in the W+jets topology with a leptonically decaying W boson are classified as signal-like by four parallel analyses based on likelihood functions, matrix elements, neural networks, and boosted decision trees. These results are combined using a super discriminant analysis based on genetically evolved neutral networks in order to improve the sensitivity. This combined result is further combined with that of a search for a single top quark signal in an orthogonal sample of events with missing transverse energy plus jets and no charged lepton. We observe a signal consistent with the standard model prediction but inconsistent with the background-only model by 5.0 standard deviations, with a median expected sensitivity in excess of 5.9 standard deviations. We measure a production cross section of 2.3-.06_-0.5(stat + sys) pb, extract the CKM matrix element value |V(tb)| = 0.91+0.11_-0.11(stat + sys) +/- 0.07(theory), and set a lower limit |V(tb)| > 0.71 at the 95% confidence level, assuming m_t = 175 GeV/c2.
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