Typed decision-making tasks in agents, such as UI element selection, product recommendation, and chart matching, require models to choose from a set of discrete candidates. While prior work demonstrates that text-only System One models achieve four key properties including candidate-order invariance, scalability, and cache reuse via separate request-candidate encoding, extending them to multimodal settings where candidates are visual remains underexplored. We introduce Iris, a framework that accommodates image, text, or hybrid candidates while preserving the core decision module. We prove that order invariance and exact cache reuse hold for any per-candidate encoder under Iris, and derive the closed-form latency reduction. We construct a visual-candidate benchmark from Multimodal-Mind2Web (K=16, deduplicated, order-shuffled, three generalization splits). Independent encoding (Iris) achieves 78.4 / 72.1 / 74.8 percent accuracy with zero-flip rate under candidate reordering. Joint encoding reaches 90.6 / 89.5 / 91.6 percent but suffers an 8 to 10 percent answer-flip rate when shuffled. To bridge this gap, we propose a design that encodes each candidate conditioned on the request state without inter-candidate cross-attention; it preserves strict order invariance, enables forked cache sharing, and attains 91.7 / 86.5 / 90.0 percent accuracy at one-third of OneJev latency with calibrated null probabilities (AUROC 0.93 to 0.97). Reusing image candidates across requests cuts latency by 37x at K=256 and 191x at K=2048. On MetaEncoder benchmarks, Iris-4B achieves 100 percent on JevBench original and easy, outperforming 30B MetaEncoder and 27B OpenJev. Finally, we resolve a systems bottleneck on Ampere GPUs: reformulating Qwen3.5 patch-embedding Conv3d into its exact matrix-product form accelerates processing by 350x. Code, data, and checkpoints: https://github.com/lllfx/Iris.

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