Abstract
arXiv:2605.18838v2 Announce Type: replace Abstract: Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale $N_c$, capabilities anticorrelate; above it, they cooperate. $N_c \approx 3.5$B parameters [2.9B, 13.4B] (bootstrap 95\% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift $N_c$ independently: curated training eliminated the coupling dip between Qwen generations (0.025 $\to$ 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6\% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier ($r = +0.72$, 34 models, 10 labs). A proof-of-concept intervention confirms the bottleneck is exploitable: adding a single truth-direction vector at the identified layer corrects 60\% of misaligned outputs in the tax phase with zero retraining -- a surgical, per-inference correction that requires no weight modification. Code, data, an open-source steering CLI for any open-weight model, and an interactive dashboard for phase diagnosis are released: https://zehenlabs.com/cape/.