Prompt Architecture Determines Reasoning Quality: A Variable Isolation Study on the Car Wash Problem

In a previous study [Jo, 2026], STAR reasoning (Situation, Task, Action, Result) raised car wash problem accuracy from 0% to 85% on Claude Sonnet 4.5, and to 100% with additional prompt layers. This follow-up asks: does STAR maintain its effectiveness in a production system prompt? We tested STAR inside InterviewMate's 60+ line production prompt, which had evolved through iterative additions of style guidelines, format instructions, and profile features. Three conditions, 20 trials each, on Claude Sonnet 4.6: (A) production prompt with Anthropic profile, (B) production prompt with default profile, (C) original STAR-only prompt. C scored 100% (verified at n=100). A and B scored 0% and 30%. Prompt complexity dilutes structured reasoning. STAR achieves 100% in isolation but degrades to 0-30% when surrounded by competing instructions. The mechanism: directives like "Lead with specifics" force conclusion-first output, reversing the reason-then-conclude order that makes STAR effective. In one case, the model output "Short answer: Walk." then executed STAR reasoning that correctly identified the constraint -- proving the model could reason correctly but had already committed to the wrong answer. Cross-model comparison shows STAR-only improved from 85% (Sonnet 4.5) to 100% (Sonnet 4.6) without prompt changes, suggesting model upgrades amplify structured reasoning in isolation. These results imply structured reasoning frameworks should not be assumed to transfer from isolated testing to complex prompt environments. The order in which a model reasons and concludes is a first-class design variable.

Large language models (LLMs) have become increasingly used for various tasks, often coupled with Chain-of-Thought (CoT) prompting to boost accuracy. Recent work has shown that high label-prediction accuracy does not guarantee correct intermediate reasoning, and the causes of reasoning flaws vary from sample to sample, yet existing remedies either focus on a single domain or assume that one flaw type applies uniformly across samples. A simple mitigation method is to provide the model with the correct answer, but we show that this yields no consistent improvement in reasoning quality. This indicates that the problem cannot be fixed by LLMs' awareness of answers, and must instead be addressed through the structure of reasoning. Motivated by this, we propose CRAFT (Consensus Reasoning knowledge graph Aggregation for Flaw-aware Trace synthesis), which aggregates the consensus components shared across multiple candidate reasoning traces to synthesize improved ones. CRAFT consistently improves label-prediction accuracy on both logical and mathematical reasoning benchmarks, outperforming most baselines, while its post-processed traces achieve higher quality under fine-grained benchmark evaluation.

Asked whether to walk or drive to a car wash 50 m away, most language models say walk, forgetting that the car has to be there. Such failures are usually measured by accuracy on questions where the hidden constraint applies. We show that this is misleading: a model can answer these questions correctly without reasoning about the constraint at all, simply by favoring the cautious option. We instead ask whether a model's decision changes when the constraint is removed. We test this at three levels of control: log-probability sweeps on open-weight models, a 500-prompt stress test, and CORE, a new human-validated benchmark of minimal constraint-present/constraint-absent pairs. The picture is consistent. The constraint nudges decisions rather than governing them. Models still miss presence constraints like the car wash, yet elsewhere they apply constraints that are not there. As a result, standard accuracy flatters all ten models we evaluate and reorders their ranking, and prompting fixes that look effective largely vanish under paired scoring. Claims about hidden-constraint reasoning need paired evidence.