Irreducibility of the Exposed-Point Variety of a Discotope

A discotope is a finite Minkowski sum of linear images of Euclidean unit balls. We prove that, when every summand has intrinsic dimension at least two, the complex Zariski closure E of its exposed points is irreducible, without a genericity assumption. The proof uses the real-analytic support-point map on the connected complement of finitely many subspaces of codimension at least two. Under an explicit generic maximal-rank condition on all summand spans, every boundary point expressible as a sum of summand-boundary points is a limit of exposed points; hence the purely nonlinear part S equals E and is irreducible. This proves Gesmundo-Meroni Conjecture 8.2 (The Geometry of Discotopes, 2022) and Conjecture 1 in Meroni's contribution to Oberwolfach Report 15/2023, exactly frozen UnsolvedMath record OWR-12697711-006. Segment summands are excluded, and S=E may fail for nongeneric representations. The entire complex critical locus, birationality, degree, zonoid recognition and the adjacent rank-one convexity question are not resolved here. This five-page English preprint credits the existing support-face description and standard analytic inputs. It was developed with AI assistance and self-audited; 255 exact regression checks supplement the written proof. It is unrefereed, without independent review, formal proof-assistant verification or an absolute-priority claim.