MORP-02: Native Defect Extraction, Defect-Completed Compactness, Profile Splitting, Harmonic-Pressure Quotients, and Minimal-Profile Existence

Native Defect Extraction, Defect-Completed Compactness, Profile Splitting, Harmonic-Pressure Quotients, and Minimal-Profile Existence

MORP-01 reduced the minimal-obstruction construction to four modules (M-XTR, M-COM, M-TR, M-RIG); this round attacks the first two. The core difficulty is subtle: a dangerous terminal state may be nonzero at some pre-singular moment, yet a general spacetime compactness topology can forget it entirely. What's needed is a topology simultaneously "generated by native Navier–Stokes quantities," "compact enough to reach a minimizer," "strong enough not to erase an already-extracted obstruction," and "flexible enough to preserve a pure-defect limit." It builds an explicit defect-completed compactness topology, proving strong local L³ compactness of velocity and strong L^(3/2) compactness of active Calderón–Zygmund pressure under standard uniform locally-suitable-weak-solution bounds (harmonic pressure is kept as an independent weak-quotient/tail coordinate). It extracts a nonnegative dissipation-defect measure from weak H¹ convergence, proves a time-slice extraction barrier theorem and a thickened state/defect-carrier theorem, giving a conditional minimal-profile existence theorem.