Boundary Screening Bounds the Evidence in Span Masking but Does Not Predict Linear-Probe Representation Quality at Small Scale

Span masking is usually justified informally: contiguous masks are said to force phrase-level rather than token-level inference. We make that argument quantitative and then test it. A boundary-screening theorem shows that the evidence a context carries about a masked set passes entirely through the block boundaries, so it scales with the number of masked blocks rather than the number of masked tokens. The downstream prediction this suggests, registered with decision rules fixed before any run, is refuted. Across a sixteen-fold range of span length at a fixed masking ratio, probe accuracy varies by 0.80 points, a fraction of the 2.0 to 4.3 point changes the same design resolves from auxiliary objectives and from training length. Mask geometry therefore bounds the available evidence without predicting tested representation quality at this scale. Three predictions do hold: the closed form for Gaussian chains matches direct computation to 10-13 nats, a radial conservation law for cosine objectives is recovered in a trained transformer to within 3 percent, and an auxiliary masked-language term improves lexical probes while degrading semantic ones. Encoders are 4.5M parameters trained on 74M tokens, a scale at which the random-initialised baseline is already strong.