Abstract: The constraints are set up both with (1) conformal thin sandwich data, and with (2) extrinsic curvature data, using the new tensor splitting in the latter case. Until 1999 there was no satisfactory thin sandwich picture; and the existing extrinsic curvature method, though yielding valid data, was an ansatz rather than a truly fundamental method. Now both approaches are fundamental, fully consistent, and fully conformally covariant. The "densitized lapse function," rather than the ordinary scalar lapse function, will be seen to be the "c-number" undetermined multiplier of the Hamiltonian constraint in the canonical action principle. In turn, these results cast the third Bianchi identities into causal first order symmetric hyperbolic form for conservation of the constraints, an outcome one seeks in vain in the standard approach. Failure of the constraints to be conserved causally has, in fact, heretofore been treated by mathematically minded relativists using either silence or hand-waving. Now causal conservation is a result, as we know it must be. It must be said, however, that the "best" form of the evolution equations is still something of a mystery.