Finite-Horizon Structures XV: Kähler-Compatible Geometric Supports and Pre-Metric Threshold Order

This article develops the Kähler-compatible support layer of the Finite-Horizon Structures programme. It studies how a regular projective Y-structure may be equipped with an external Kähler support geometry without deriving that metric structure from the projective core itself. The paper shows how the logarithmic representative log Y determines, relative to a chosen Kähler support, a metric gradient, a symplectic dual vector field, regular threshold hypersurfaces, maintained superlevel domains, support volumes, and adapted logarithmic normal forms. The central result is that directional threshold order remains pre-metric: it is governed by Y, its logarithmic coherence one-form, admissible transport, maintained domains, reachability envelopes, and fronts, not by the Riemannian signature of the added support. This article forms part of the Ranesis framework developed by Alexandre Ramakers.