Emotion as Geometric Onset: How Affective States Generate the Spaces They Inhabit

Existing approaches model emotions either as regions in a pre-given affective space (circumplex, PAD, Riemannian manifolds) or as sub-cognitive impulses without intrinsic geometry. Both miss a constitutive feature of affective experience: emotions generate the geometry in which they subsequently operate. This paper develops a formal grammar of emotional onset processes. Its central thesis is that emotions are neither geometric (points on a manifold) nor pre-geometric (undirected gradients), but the phase transition between both—the specific mode in which Proto-∇ (directed difference under continuity) crystallizes into a locally structured, inhabitable state geometry. Formally, we define local geometry as a minimal triplet(g_x = (A_x, d_x, \Theta_x)) consisting of admissibility structure, local quasi-metric, and topological signature. An emotion is then characterized by a specific onset signature(\mathrm{Sig}(e) = (\Delta A, \Delta d, \Delta \Theta)) specifying which components change, in which direction, and under which conditions. We prove a reduction theorem showing that all fixed-space models are special cases with (O_g = 0). The paper provides: (i) a taxonomy of six fundamental geometry-generating patterns (Angst, Wut, Trauer, Scham, Freude, Liebe), each distinguished by its onset signature; (ii) a formal bridge to the regime-operator framework, identifying emotions as the most powerful class of intrinsically coupled operators; (iii) empirically motivated operationalization paths; and (iv) explicit falsification targets. The paper should be read as a theoretical and programmatic contribution to a regime-sensitive affective pragmatics, supported by convergent motivating evidence rather than offered as a completed measurement framework.