**D I think Alan can answer this**

Yes, [-0.5, 0.5]^3 is entirely safe in that it corresponds to acos(0.50) = 60° to acos(-0.5) = 120° angles between the original data vectors. But any correlations outside [-0.5,0.5] can induce constraints on the other rhos.

**D is there something sacred in cos() or are there others?**

Expanding the algorithm would probably mean either:

1) using the equation for the determinant of the NxN.

**D How big is N? Do determinants work these days? Last time I did determinants was at school, maybe I missed something.**

2) doing an eigendecomposition of the matrix with a sensitivity analysis WRT the values and find the perturbations of the values that bring all the negative-valued modes to zero.

**D negative e-values -> 0?**

3) Expressing the constraint in terms of acos(rho) angles (and distributions of those angles) with combinatoric logic for which chains of rhos are mutually incompatible.

**D cos() is a wiggly function going to eternity; what about [$]\rho = tanh(\theta)[$]?**

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