Chapter 57: The Universal Defect Tuple

the relevant chapter introduced the defect tuple d = (d₁, d₂, d₃, d₄) as a universal regime classifier and identified eight canonical fluid regimes. This chapter develops the defect tuple itself: its mathematical structure, its transformation properties, its role as the master coordinate on the phase space of matter. The tuple is not merely a convenient label. It is the canonical projection of the full defect functional onto the four geometric axes of T², and the projection is both complete and minimal—no fifth component exists, and no component is redundant.