A multimodal large language model (MLLM) forecaster takes a forward-looking scenario as a soft constraint whose influence across the horizon is uncharacterized and untunable. A practitioner running a twelve-month stress test cannot tell whether the scenario shapes the forecast for twelve months or twelve days, and existing accounts of autoregressive error offer no remedy at inference time. Under two assumptions, we prove a closed-form Lipschitz upper envelope on the scenario drift, the gap between paired-seed forecasts that differ only in the scenario. Its two identifiable parameters partition behavior into bounded, linear, and exponential regimes. Their effective estimates place three open-weight MLLMs at the edge of the bounded regime, where drift keeps compounding over the observed horizon. A second bound, on the excursion within a chunk, motivates a stabilization heuristic, periodic re-injection of the scenario. Re-injection enlarges drift, and length-matched random text shrinks it, which falsifies the heuristic and is consistent with the bound. An attention diagnostic with a decision rule fixed in advance links the drift to attention on one of three architectures. No single attention-dilution account therefore explains the drift, while the envelope holds whatever the mechanism. In place of text re-injection, we propose Visan (Visual Anchoring), a multimodal prompt that renders the lookback, the scenario, and the historical context as one chart. On What If TSF, Visan reduces forecast error on four of five MLLMs, significantly on three. On the long-horizon MacroLens benchmark, it beats text re-injection on four of five and the text-only prompt on two. A controlled decomposition shows that neither the directive nor the digit precision produces the gain, and that the chart is the only image format that hurts no model.
TBD