Global structure of the regular solution space

Determine the maximal extent, possible noncompact ends, and distribution of primitive quantized rays in the physical flux image and regular solution space of the cohomogeneity-one GMMW AdS3×M8 ansatz, including whether the certified finite-ratio region connects to an analytic seed through a validated continuation.

Background

The paper establishes local four-parameter analytic families of regular non-polynomial solutions and proves that an explicit finite-ratio box in the fully positive curvature sector lies inside the physical flux image. It also reconstructs candidate endpoint data rationally from compatible fluxes, but endpoint reconstruction does not by itself guarantee an interior solution with H>0 and D<0.

Numerical continuation suggests connections among several representatives, yet it is not carried out as a validated continuation at fixed compactification data or through the integral flux lattice. Consequently, the global topology and extent of the regular solution space, including the behavior at noncompact ends and the arrangement of primitive quantized flux rays, remain unresolved.