Presupposed vs Asserted Falsehoods: Measuring Premise Sycophancy in GPT-4o, Claude Sonnet 4.5, and Gemini 2.0 Flash

Large language models exhibit sycophancy: a tendency to agree with user-supplied claims over factual accuracy. Prior work studies sycophancy when a false claim is asserted or when a user voices disagreement, always placing the false content in the assertoric part of the input. This study asks whether frontier models are more sycophantic when a false premise is syntactically presupposed inside a question than when the same premise is stated as a declarative assertion. In a within-subjects design, 1,793 responses were collected from GPT-4o, Claude Sonnet 4.5, and Gemini 2.0 Flash across two studies and scored on a four-point ordinal rubric using a blinded LLM judge with independent cross-validation (80.4% exact agreement; Spearman rho = 0.774). On well-known historical myths (Study 1), all three models corrected at near-ceiling rates regardless of framing and no presupposition effect appeared. On nuanced or contested claims (Study 2), presupposed-false prompts produced acceptance rates of 24.7% versus 12.2% for asserted-false prompts (chi-square = 17.855, p < .001), largest for GPT-4o and smallest for Claude Sonnet 4.5. Two secondary findings: presupposed prompts caused models to engage with false content before correcting it more often (p = .003), and definite-description triggers produced the largest condition gap among presupposition types (H = 15.131, p < .001), matching linguistic predictions about presupposition projection strength. Claim complexity gates the effect: invisible on memorized myths, clear on nuanced claims. These findings indicate that the syntactic packaging of a false claim, not only its content, determines whether models correct or accommodate it, and that sycophancy benchmarks should include presupposed-false content.