Inhabited Space as a Constrained Generative System with Recursive Border-Reading: Border Profile, Regulatory Operator, and the Sfasamento Measure

Reduction of inhabited space to minimal structural content under irreversible constraints. Urban pixels classified by border profile: traversable arcs, direction (σ or ω), and accessibility of the border. T3-dominant, T2 local. Regime R2 (branched attractor). The pixel is the minimal point where a habitable difference meets a traversable limit. The observable η = d_eff/d_reg measures border activation. The regulatory operator (zoning, building code, traffic regulation) is identified as an asymmetric ω-operator that filters arcs without generating borders, the first domain where the border is simultaneously traversed, read, and modified under the same limit. This defines the U-series: systems with recursive border-reading. The sfasamento measure Δη = η_obs − η_struct quantifies the distance between regulatory imposition and structural reality. Validated on Barcelona (superilles), Kalamazoo (pedestrian mall failure), and Isfahan (pedestrianisation, arc fusion). All three outcomes predicted by the border profile without additional axioms.