This manuscript develops a structural framework for semiprime numbers, i.e. integers of the form S = pq, by organizing several exact projection layers into an operator-resolution hierarchy. The framework includes square-shell coordinates, Fermat and P-map geometry, compatible residue branches, digital quotient layers, Type C center structure, logarithmic mirror geometry, hyperbolic closure, and integer-phase structures. The guiding idea of Version V10.1 is structural resolution. A single projection usually exposes only a partial shadow of the hidden factor configuration. When several projections and error channels are coupled, factor-equivalent objects such as the factors, center displacements, logarithmic opening parameters, factor-ratio shadows, and integer phases may become increasingly constrained as shadows, intersections, double-zero events, or consistency patterns. This is described as emergent visibility under an operator-resolution hierarchy. The logarithmic layer is treated as a central coupling level. It provides a mirror geometry around the logarithmic center, connects to the factor-ratio shadow, admits a hyperbolic closure into Fermat coordinates, and supplies the parameter axis on which one-sided and two-channel integer errors can be studied. These structures do not by themselves yield a factorization method; they provide a coordinate system in which the relation between smooth mirror geometry and discrete integer constraints can be analyzed. This public preprint version is a consolidated structural reference. It does not claim a new factorization algorithm, an efficient search rule, a complexity result, or any cryptographic implication. Factorization is discussed only as a possible emergent visibility phenomenon under coupled structural resolution.
Rolf-Peter Rieger (Thu,) studied this question.