DRC-06: Persistent Core Dilution, Backward Concentration, Absolute UV Core Carriers, and Core-Reuse Rigidity

Persistent Core Dilution, Backward Concentration, Absolute UV Core Carriers, and Core-Reuse Rigidity

DRC-05 reduces the core of the main unresolved dynamic reservoir to R_DIL. This residual originates because a Type-I singular core may contain a shell or high-frequency state with strong absolute local vorticity mass, while its globally normalized share tends to zero (since more enstrophy exists elsewhere). Previously encoded via a quantity like β_c(t) = global state mass of the selected core shell / total global enstrophy, a small β_c was treated as a possible local/global ancestry failure. This round points out a normalization error in that interpretation: for singular-core ancestry, the primary state variable need not be a global probability share. Using Barker–Prange's Type-I enstrophy concentration and backward propagation, replaces the globally-share-normalized core carrier with an absolute scale-invariant local core carrier; combined with CSP-02's local low-frequency exclusion, obtains an absolute UV core carrier above the parabolic frequency. Proves a geometrically concentric backward core-reuse chain, showing a vanishing global enstrophy share does not erase this local ancestry. Barker–Prange's finite Type-I singular-point bound gives a finite final spatial-center branching.