Modern GUI-agent frameworks achieve strong desktop task performance with frontier API models, yet persistent control information often remains implicit in growing interaction trajectories. At each step, the planner reconstructs the active task stage, accumulated evidence, and runtime feedback before deciding the next action. This dependence becomes more pronounced under weaker local reasoning backbones. Across four representative state-of-the-art frameworks, replacing GPT-5 with Qwen3.5-9B reduces average OSWorld SR-100 from 60.9\% to 37.7\%. Trajectory annotation further identifies at least one control failure in 91.6\% of failed trajectories. To address this problem, we introduce LocalLSTC, a training-free architecture that organizes control by temporal scope, maintaining persistent cross-step state to guide short-term execution commitments. Long-Term Control maintains the active subgoal, subgoal-aligned evidence, and runtime feedback across interactions, while Short-Term Execution realizes bounded commitments for the current step. Long-to-Short Planning forms each commitment from persistent state, and Short-to-Long Control integrates execution outcomes back into that state for progress assessment, recovery, and termination. With Qwen3.6-27B, LocalLSTC reaches 64.7\% SR-100 on OSWorld and 65.3\% on WindowsAgentArena, outperforming the strongest prior local results on both benchmarks. Ablations further support contributions from mechanisms on both sides of execution. These findings identify temporal organization of control information as a distinct architectural dimension for locally deployed GUI agents.
Large language models are increasingly deployed on local hardware for privacy, cost, and accessibility reasons. Yet many evaluations emphasize accuracy while fewer quantify local runtime and energy, characterize failure modes, or apply paired statistical comparisons under controlled conditions. This paper presents a controlled, documented procedure for evaluating locally hosted LLMs on mathematical reasoning. It combines fixed inference settings, hierarchical answer extraction and verification, explicit failure-mode classification, and per-question resource measurement, and reports accuracy with paired significance tests and effect sizes. We demonstrate it in a preliminary study of three compact open-weight models under five billion parameters, Gemma3:4b (Google), Phi3:3.8b (Microsoft), and Qwen3:4b (Alibaba), across datasets spanning Grade 8 Math, Calculus I, and Advanced Probability and Statistics. All models ran through the same local inference server on one workstation, using a shared prompt template, controlled settings, and a matched question set per dataset. No single model dominates. Qwen3:4b is most accurate on two datasets and Gemma3:4b on Calculus I, yet Gemma3:4b returns roughly three times more correct answers per watt-hour than Qwen3:4b on every dataset while generating far fewer output tokens; Qwen3:4b requires substantially more generation time, energy, and output per question. Phi3:3.8b is substantially less accurate on all three datasets; its low extraction-failure rate indicates incorrect answers rather than unparsed output, though we caveat possible prompt-format effects. These preliminary findings indicate that accuracy alone is an insufficient basis for selecting a local model.