This appendix proves Theorem 5.2. The proof involves two halves: the first half proves that if then and the second half proves the converse. Both halves are required to prove the *if and only if* aspect of the theorem.

To prove the first half, we compute the elements of **R** using the definition of **R** in Eq. 5.6 and assume that The elements of **R** have the form which can be expressed as follows:

(B.1) |

where we ...

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