Shelter and Access: One-Sided, Falsifiable Interior Measures for Generated Voxel Buildings

Evaluation of open-ended building generation in embodied environments (whether the builder is a procedural generator, a diffusion model or an LLM agent) still rests on human ratings, on visual models, or on similarity to a reference solution. The first two yield no falsifiable quality claim about a single building, and similarity requires a reference solution that open-ended building does not have. None of them answers the question: can an agent with a body use this structure as a house? We propose the interior field Ω, defined by voxel geometry alone, which measures how enclosed each air cell is; it has no trainable parameters. On top of it we build two one-sided measures: shelter indicates whether a building can provide cover, and access indicates whether there exists an agent-centric path (one a player-sized body can walk) from relatively outdoor space to relatively indoor space. One-sided means the measure's house-quality claim is made in the low direction only and is falsifiable there: a low score means the building fails a necessary condition of a usable house (no cover, or no way in), a fact checkable in its geometry; a high score means only that the condition is met, not that the house is good. We also propose VoxHouse3D, a dataset of 2,007 player-built houses and 2,023 same-provenance non-house structures, taken from 28 archived worlds of real community servers, one map file each.