This note studies response-only full conformal prediction (FullCP) with no covariates or fitted predictive model, whose exact region comprises multivariate responses accepted by the conformal comparison rule. Standard conformal theory addresses validity; this note studies score-induced geometry and faithful representation when the set need not be convex. For an empirical energy-form pairwise score, the leave-one-out comparisons reduce exactly to pairwise-dissimilarity sublevel conditions that, under the stated score assumptions, share a common center; convex comparison sets then yield a star-shaped exact FullCP region. For power distances this geometry holds for β ≥ 1, and in the univariate β = 1 specialization every nontrivial fixed-bin empirical continuous ranked probability score (CRPS) FullCP region is a nonempty closed interval. Star-shapedness permits an exact ray-wise representation, and for 1 < β < 2 explicit data-checkable radial Lipschitz bounds convert finitely many certified directional searches into global inner and outer reconstructions with deterministic same-ray Hausdorff error guarantees. An analytic two-dimensional example shows how convexification can enlarge the exact accepted set, and a staged two-dimensional numerical study assesses certificate tightening and nonconvexity diagnostics without making a coverage or prevalence claim. In the frozen study, the focuswise bound tightened the generic bound by 3.4% at the median, while both remained roughly two orders above a finite-grid lower proxy.  The reconstruction results are score-specific and intended for low-dimensional multivariate outputs; no runtime improvement is claimed.
