Large Nc means Nc=3

We show that the nonperturbative solution of the SU(2) linear sigma model field theory requires color number Nc=3. Also, we show that the three-point and four-point functions bootstrap (or nonperturbatively ``shrink'') in the chiral limit to the tree amplitudes. Independently, we show that a chiral phase transition for Nf=2 requires Tc=180 MeV, consistent with the computer lattice value (173 +/- 8 MeV).Comment: 9 pages, LaTeX. Invited talk given at the Large Nc Workshop, ASU, January 200

Consistently computing the K -> pi long distance weak transition

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