Memory summaries, prompts and steering vectors set a language model's beliefs and are judged by the prediction they produce. A prediction does not say how firmly it is held. We separate a belief's content, what it predicts now, from its weight, the number of new observations it is worth: for an ideal observer, the amount of evidence behind it. In Bernoulli inference we set beliefs in nine open-weight models of 8 to 397B parameters and follow each belief with the same new observations. We argue that these models hold an answer without its evidence and recover its weight from the text they re-read. Weight therefore follows the form of the evidence and the question asked more than its amount: matched on their current estimate, a record of observations and a summary of its counts usually move apart under the same new observations, in either direction. Scale does not close the gap. Across the nine models 64 observations are worth 20 to 53 as a record and 9 to 151 as a summary, no closer to 64 at 397B than at 8B. Where no text stands behind a belief there is little to re-read: a steering vector can install a record's answer, and sixteen observations undo it where a neutral passage leaves it in place. Where reasoning first writes the counts into the context the weight returns, and the same 64 observations are worth 58 to 67 in either form. A matched answer is not a matched belief, and methods that set beliefs should be judged by the futures they produce.
Learning systems adapt quickly within a familiar family of models. The harder step is deciding, from a prediction failure, whether opening a richer family is worth its cost. We cast this as a costly sequential decision and introduce the Structural Revision Environment (SRE), which produces matched failures from noise, exceptions, change within the family or structure outside it, varies the price of expansion and the remaining horizon independently of the evidence, and admits an exact normative solution of the one-shot decision. The solution shows that revision is a value boundary, not an evidence threshold: except at the lowest prices, the richer family becomes the more probable explanation long before expanding becomes optimal. Small Transformers trained in SRE reproduce the expansion boundary from utility alone. Pretrained 7B and 8B language models fail at a definite point: their predictions carry a failure-sensitive signal that their decisions do not reflect. Told the gain of expanding, they weigh it against price and horizon only when they reason, and the one model that finishes its reasoning on the history alone still does not estimate that gain. Controlled post-training of the small Transformers moves the prior and the sharpness of predictions, and neither moves the criterion.