Tracing Prompt-Conditioned Control from Allocation to Realized Actuation in Frozen VLMs

We analyze inference-time control authority through the measurable sequence ($\mathbf{a}\to \mathbf{m}\to \mathbf{w}\to \mathbf{u}\to \mathbf{r}\to \mathbf{\ell }\to \mathbf{p}\to \mathbf{y}$). In one paired checkpoint, Dynamic-to-Uniform composition yields equal measured accuracies. Across five training seeds, the replacement changes the Prompt-derived state while retaining a zero-median allocation response and unchanged dominant allocation indices. Direct allocation and Prompt-input replacements produce downstream continuous responses at different controller coordinates, revealing a recurrent dissociation between conditioning variation, continuous allocation, realized actuation, and decision-boundary crossing.