Spherical Geometry and Holonomy Signatures in Affective Space: Computational Evidence from fMRI Emotion Trajectories

Emotional representations are typically modelled in flat Euclidean space following Russell's (1980) two-dimensional valence-arousal circumplex. The Affective Spin Bundle Hypothesis (ASBH; Radchenko, 2026) proposes that affective state space has spherical geometry (S²), with parallel transport along closed trajectories producing geometric holonomy proportional to the enclosed solid angle—a signature impossible in any flat geometry. We test this hypothesis computationally using the publicly available Emo-FilM fMRI dataset (Ma N = 29 participants, 14 films, 13 emotion categories), projecting Warriner et al. (2013) Valence–Arousal–Dominance (VAD) norms onto S² as a priori coordinates independent of the fMRI data. Eight computational tests yield four key results: (1) S²-geodesic step distances correlate with the authors’ 2D MDS trajectories at ρ = 0.704 ± 0.042 across all 14 films; (2) solid angle enclosed by affective quasi-loops independently predicts loop-closure error (partial ρ = 0.382, p = 1.4 × 10⁻¹⁰, n = 263 non-overlapping loops); (3) transitions crossing the valence equator are 2.4× larger in S²-geodesic than flat MDS distance (p = 9.2 × 10⁻¹⁵); (4) an ellipsoidal S² with density potential outperforms round S² by ΔAIC = −15.7, with separate optima for behavioral similarity (λᴅ/λv = 3.8) and holonomy dynamics (λᴅ/λv ≈ 1.1), suggesting a non-Levi-Civita connection. These results support ASBH and motivate replacing flat MDS with spherical coordinates in hippocampal-prefrontal decoding models.