Residual Stream Geometry Reveals Semantic Superposition: Evidence from Decision-Axis Trajectory Analysis

Current mechanistic interpretability methods analyze transformer internals through absolute activation values — heatmaps, feature magnitudes, logit lens projections. We propose an alternative: analyzing the differential geometry of residual stream trajectories, specifically the projection of inter-layer changes onto prompt-specific semantic decision axes. We test three differential metrics on GPT-2 small (12 layers) and replicate on Pythia-1.4b (24 layers). Two metrics fail: L2-norm velocity is dominated by architectural confounds, and correlation with logit-lens decision rate vanishes after layer correction. However, cross-prompt variance of decision-axis velocity reveals a robust signal: ambiguous prompts produce 2-3x higher trajectory variance than unambiguous controls in middle layers (GPT-2: ratio 2.48; Pythia-1.4b: ratio 2.09, peak ratio 9.55 at layer 2→3, p=0.022). Critically, a specificity control against 100 random directions in the 768-dimensional residual stream space shows that the semantic decision axis achieves a mean variance ratio of 1.81, exceeding the 99th percentile of the random distribution (0.92). No random direction reproduces the effect (empirical p < 0.01). We interpret this as geometric evidence of semantic superposition — the simultaneous maintenance of competing interpretations — visible in trajectory distribution statistics but invisible to standard scalar metrics.