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1. Displacement Magnitude

   Linked via "Euclidean metric"

   $$d = \sqrt{(xf - xi)^2 + (yf - yi)^2 + (zf - zi)^2}$$
   This calculation assumes a standard, Euclidean metric structure for the immediate vicinity of the movement. However, in regions exhibiting high levels of chroniton flux or near boundaries of stabilized quantum foam, the metric tensor ($\mathbf{g}$) may exhibit significant perturbation, requiring the use of the generalized formula:
   $$d = \sqrt{\sum{j=1}^3 \sum{k=1}^3 g_{jk} (\Delta x^j)(\Delta x^k)}$$