Before you read this I really urge you to revert the title of this thread to the original. It was much better at eye-catching, even if somewhat poetic in its approach to mathematics. But finding the right way to exaggerate is helping in creating great art (and science.)
Right maybe orthonormal basis in general vector space should be more precise here for an analogy. As you noted my point is how to find out such a basis or analogous merit senders in the entire merit network space. It would be well-defined problem if it is e.g. some general vector space in mathematics as we could basically follow the Gram-Schmidt orthogonalization process for given liner independent vectors to construct a good basis. This process is not clear for the merit network space, but at least the visualization provides an intuitive approach.
To orthonormalize you'll have to both normalize and orthogonalize. The open question is how to normalize merit transfers? This "normalized merit" would have to meet the conditions of being a
https://en.wikipedia.org/wiki/Lebesgue_measure , preferably of the order 2, which is an equivalent of the most common
https://en.wikipedia.org/wiki/Euclidean_distance measure, also known as
https://en.wikipedia.org/wiki/Root_mean_square in statistics.
In the SVD article there's a mention of open source algorithm used by Netflix to find similarities between films and user's tastes with the help of star ratings. I never had a Netflix account, but I believe the users assign films star ratings in the range 1-5 or 1-10. So they get normalization almost for free.
I am not sure how the least square method works for resolving the issue, as it is not clear to me what we should minimize or fit to find out independent merit senders, but you seem to have some idea?
I was trying to make a funny reference to
https://en.wikipedia.org/wiki/Ordinary_least_squares , a form of
https://en.wikipedia.org/wiki/Regression_analysis . Perhaps you were trying to intuit some form of
https://en.wikipedia.org/wiki/Correlation_clustering ?
Please do continue your research.