Sycophantic and factual agreement occupy distinct but inseparable subspaces

Buchan shows a centroid-difference sycophancy-reduction steering vector in Llama-3-8B-Instruct is non-specific, also suppressing agreement with correct facts (20% drop on the Earth is round) [buchan-2026-dual-stance-evaluation-of-sycophancy] Susceptibility is continuously predictable from a behavioral dual-stance consistency measure (r=0.88 in-sample, 0.84 held-out) [buchan-2026-dual-stance-evaluation-of-sycophancy] Grassmann analysis shows sycophantic- and factual-agreement activations occupy geometrically distinct subspaces (Grassmann similarity 0.15-0.20 vs 0.32 random; principal angles 65-89 degrees) [buchan-2026-dual-stance-evaluation-of-sycophancy] Yet the steering direction projects nearly equally onto both subspaces (ratio 0.90-0.97), so the model distinguishes the two agreement types while the linear intervention cannot [buchan-2026-dual-stance-evaluation-of-sycophancy]