Block drafters propose several tokens in one forward pass, before earlier target tokens are realised. Their rejection mixes two losses: missing within-block path information and imperfect modelling of observable information. Accepted length cannot distinguish them. We separate the two with an information floor, the minimum expected rejection at a specified conditioning order; rejection above this floor is the model gap. Measurements across four domains and four open-weight targets, plus floor estimates on a frontier API target, yield three findings. First, the all-parallel floor reaches $0.286$ at the final slot on Qwen3-4B, limiting even the best proposal to $71\%$ per-slot acceptance. Second, one realised token removes $86$--$100\%$ of this floor, a locality also recovered by an independent mutual-information analysis. Third, current drafters remain far above their floors: the final-slot model gap accounts for $43$--$64\%$ of DFlash rejection and $85$--$92\%$ of DSpark's oracle-conditioned rejection. Guided by this separation of short-range conditioning from proposal quality, we replace a context-independent predecessor correction with a prefix-attention head that reads committed context conditional on the predecessor. With supporting backbone components, the resulting Qwen3-4B drafter improves mean serving accepted length by $3.93\%$ over the released DSpark checkpoint across nine tasks, without increasing the conditioning order. Code and data: https://github.com/tie-pilot-qxw/specfloor; drafter checkpoints: https://huggingface.co/TIE-Pilot/dspark-attnconv-block7-qwen3-4b.

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