  The characteristic hole concentrations x_opt = 0.16 and x_c = 0.19 in the
under- to overdoped transition regime of cuprate superconductors are shown to
be intimately interrelated by mesoscale organization of bond-like RVB arrays
extending over 3 x 4 copper sites and comprising 2 holes spaced by 3a_0.
Columnar organization maximizes T_c but reduces the superfluid stiffness, while
zigzag (tweedy) organization maximizes the superfluid stiffness at reduced T_c.
The latter goes hand in hand with the closure of the pseudogap. Columnar and
zigzag mesoscale organizations of the bond-like RVB arrays are displacively
transformed in each other between x_opt and x_c by weak overdoping.
