Variance fraction captured by the first two principal components

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Adding the first two explained-variance fractions gives 0.9498998129, or about 94.99% of the variance in the centered representation analyzed. This measures compression of that particular trajectory into two linear directions. It does not mean those directions account for the same fraction of total model behavior or capability.

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Original context

The two leading PCA explained-variance fractions sum to

Appendix C. Why the bare divergence condition needs specificity

Consider the scalar recurrence zn+1=azn+1−a with z0=2 and 0<a<1. Its solution is zn=1+an. It changes internally, differs from its original value at every subsequent finite step, and never returns to 2. A program could repeatedly report its current value without changing this algebra. Thus permanent difference from an initialization is mathematically broad, not peculiar to the present model.

0.8109369033497655+0.13896290956024188=0.9498998129100074.

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