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First we extract the long-distance (LD) weak matrix element from certain dataand give compatible theoretical estimates. We also link this LD scale to thesingle-quark-line (SQL) transition scale and then test the latter SQL scaleagainst the decuplet weak decay amplitude ratio. Finally, we study LD decay.All of these experimental and theoretical values are in good agreement. Wededuce an average value from eleven experimental determinations compared to thetheoretical SQL values average.Comment: 19 pages, 9 figures minor change to the Conclusions and abstract  sectio

CONSISTENTLY COMPUTING THE K → π LONG DISTANCE WEAK TRANSITION