Anthropic’s Verbalizable‑Workspace paper showed that a model’s middle layers carry a dictionary of directions that causally steer its output. The study left key questions open: how far forward the steering reaches, when the structure forms during training, whether it transfers between models, and how it scales. We measured all four on open models and derived every number from the committed result files, providing interactive charts.

The core method, the J‑lens pipeline, injects a nudge into a residual stream at layer ℓ and records the resulting shift in the final token probability. Averaging over many prompts creates a matrix Jℓ that acts as the layer’s dictionary of hermosa steering vectors. Two metrics summarize each dictionary: CKA (centered kernel alignment) evaluates geometric similarity, and PR (participation ratio) counts effective directions. For example, a 4,096‑entry dictionary typically spans 200–600 effective directions, giving the layer its capacity.

Temporal analysis reveals that a nudge’s influence decays with token distance Δ. At Δ = 1, only 3–6 % of the immediate effect survives in the deepest layers, and beyond Δ ≈ 12 the influence plateaus within a 128‑token window. These results confirm that middle‑layer steering is both strong and short‑lived, and they show that the workspace structure emerges without supervision.

These findings were produced with minimal manual effort, leveraging an agent to design, run, and visualize experiments, and are fully reproducible via the provided GitHub repo and data.