One Compact Amoeba Intersection, Several Mixed Cells

We give explicit obstructions to assigning one binomial system to a connected compact intersection of amoebas. For f=w-1 and g=(z-10)(z-12)(z+11)(z+13)-525w, the entire amoeba intersection is a single compact interval with four distinct real torus solutions. The canonical Ronkin spines have four transverse intersections, each dual to a fully mixed cell of volume one, while the normalized mixed Monge-Ampere mass is four. Every binomial system from any single fully mixed cell for these Newton polytopes has at most two real solutions, even after coarsening. Thus the single-binomial real-preserving correspondence in AIM A.2 (UnsolvedMath v1.6.0, AIM-GEOMETRY-0322) is false. For every d>=2, a related construction gives one compact component of mass d with d unit canonical-spine cells. The volume comparison fixes the canonical Ronkin-spine convention: arbitrary coarsenings may match complex mass. We do not claim a whole-record closure of the source's unspecified volume formulation. The first Newton polytope is a segment; unions of start systems, full-dimensional-support modifications and valid patchworking/lifting theorems are excluded. Classical local mass, spine facts and known real-homotopy limitations are credited. This six-page English preprint includes 1,104 exact standard-library checks supporting the written analytic proofs. Developed with AI assistance and self-audited, it is unrefereed, without independent review, proof-assistant verification or absolute-priority certification.