The Price of Verification in Budgeted Perception: Checking Costs What Looking Costs

An agent under a per-decision token budget holds a cheap description of each observation and re-reads the observation when a question demands it. We price the half of that bargain that is left unpriced: establishing whether the description is true. On an interface that meters tokens and re-transmits the observation on every call grounded in it, any verifier whose verdict depends on the observation must pay that transmission, so the price of verification relative to the price of the channel is bounded below and tends to one: checking costs what looking costs. Both premises are measured rather than assumed. The observation is most of the bill, identified inside a single run as the difference between a grounded and an ungrounded verdict call, and the measured ratio clears the floor those terms predict on every open backbone we test. That an observation is re-charged at all is audited on every provider endpoint the router will pin, and the audit turns on a distinction the obvious test misses: asked to serve the identical call twice, four of seven backbones have an endpoint that returns the observation as a cache read; asked a different question about the same frame (which is what a verifier does), only two do. So the assumption holds, for the call the theorem is about, on five of seven backbones, and where it fails it fails at the discount our own proposition predicts in advance. That cache then expires within minutes, which is shorter than the deferral a stored description exists to create. Pinning the provider also separates what belongs to the model from what belongs to the vendor: between endpoints of one model the dollar price of an identical call varies twofold and one endpoint tokenises the same image nine per cent shorter, while the ratio the theorem bounds moves by 0.012. A price, however, is only half a verifier. Normalising by how much a verdict actually discriminates separates two quantities that behave quite differently: the nominal ratio is pinned by the interface, moving little across an order of magnitude of scale and uncorrelated with it, while the discrimination varies widely between backbones and is a property of the individual model. The price of a verdict belongs to the interface and its value to the model; only the second can improve, and yield saturates on most backbones before it does.