Architectural design increasingly adopts generative AI (GenAI) for floorplan generation, an early-stage design task exploring how spaces should be organized for use. Yet fidelity objectives inherited from native visual and geometric generators do not automatically capture this design purpose. This organization remains largely implicit in generated representations, limiting direct evaluation and feedback. Drawing on space syntax, an established architectural design theory, the Space Syntax Integration Operator (SSIO) recovers convex-space access graphs across heterogeneous formats. This theory-grounded shared intermediate representation, which we call a design container, supports evaluation and model understanding of spatial design. Applying SSIO to four residential corpora spanning 15 countries reveals public spaces' integration levels are highest, with corpus-dependent distributions. These patterns underpin the RPLAN-SSI benchmark, an empirical design reference system assessing population-level functional-profile alignment (IPD) and within-plan public-space advantage (PIA). Comparison with this residential reference reveals a design gap: public spaces in generated floorplans have a smaller integration advantage over other spaces. To address this gap, Space Syntax-Guided Post-Training (SSPT) provides a plug-and-play design-learning interface: SSIO-derived RL feedback improves IPD and PIA across five heterogeneous diffusion backbones while preserving native mechanisms. We further discuss how this approach may inform GenAI applications in other design domains.

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