Paper 49K: Native Refinement Operator for the 642 → 2562 Holosphere Shell Alpha-Blind Topology, Boundary–Interior Label Structure, and Native Transfer Retention

Paper 49K constructs an alpha-blind refinement operator from an inherited 642-vertex closed triangulated spherical shell to its exact midpoint-refined child. Closed triangular incidence and Euler topology give the recurrence V prime equals 4V minus 6, producing 2562 child vertices. The same recurrence yields the preserved count offset 2, so the adjusted child count is exactly four times the adjusted parent count. A separately declared four-state boundary-interior label grammar provides mixed-sign cancellation, while a three-sector audit gives coherent multiplicity 3. The sparse parent-to-child operator is nonnegative, constant preserving, antipodally covariant, and compatible with the symmetry subgroup retained by the triangulation. An eleven-mode transfer audit gives a native residual burden of 0.013195238294667911, determinant-normalized retention of 0.9926915012784386, and alpha-blind native scale of 0.007303588589455189. Auxiliary TDR, VROS, triadic, topology, firewall, and ancestry-ablation audits satisfy all 14 declared commissioning contracts. After the forward artifacts were locked, comparison with Paper 49D showed exact agreement in the child-shell count and two-unit offset. The native retention and scale remained approximately 0.223 percent above the corresponding Paper 49D values. Paper 49K therefore provides conditional structural recovery of the Paper 49D shell recurrence and count offset, together with a direct finite-mode transfer metric, but does not recover the exact Paper 49D retention or derive the fine-structure constant. The remaining task is a mode-converged operator that explicitly couples the boundary-interior, TDR, and VROS sectors before held-out comparison.