Affective Spin Bundle Hypothesis (ASBH): Spherical Geometry and Holonomy in Affective Semantic Space

Existing models of affective space—Osgood's semantic differential (EPA), Russell's circumplex, and Affect Control Theory (ACT)—describe the structure of affective meaning, but not the geometry of transitions between affective states. Why does the path anxiety → anger → relief produce a different outcome than the direct path anxiety → relief, even when endpoints are identical? The Affective Spin Bundle Hypothesis (ASBH) proposes an answer: affective transitions are organized as parallel transport on a principal fiber bundle over the sphere S², and the difference in outcomes is holonomy, computable via the solid angle. The hypothesis is developed at three levels. Part I asserts the spherical geometry of EPA space and derives the core prediction ΔRT ∝ ΔΩ₀ (reaction time facilitation in semantic priming is proportional to the solid angle subtended by the prime–target–context triangle on S²). Part IIA derives the frame bundle structure (c₁ = 2, total space SO(3), Levi-Civita connection) as a mathematical consequence of the base manifold, given one interpretive postulate: modal realization corresponds to orientation in TₓS². Part IIB identifies Ukhtomsky's dominance principle as a candidate for the neural connection (mapping problem, four formalization steps). Twenty-six computational analyses on five independent datasets (ACT, Warriner VAD, SPAML, Lancaster Sensorimotor Norms, SWOW-EN18, and the Semantic Priming Project) provide moderate support for Part I: (1) S² angular distance significantly predicts RT facilitation in semantic priming (SPP, N = 2,622, r = −0.055 to −0.067, p < 0.001), surviving control for associative strength (partial r ≈ −0.05); (2) natural free-association chains cue→R1→R2 show Ω₀ = 24.8° vs. 47.1° in randomized counterfactuals (SWOW, N = 552,287, d = −0.33); (3) strong associations cluster within a single octant of S² at 3.43× the rate expected by chance. EPA vector norm is an independent predictor, motivating S² × ℝ₊ as a necessary extension. Eleven specific predictions are derived with an ordered testing sequence and a pre-specified retreat hierarchy.