No Usable Linear "Capitulation Direction" in Two Small LLMs: A Validation Protocol for Activation-Steering Claims, and a Cross-Family Behavioral Study of Sycophancy Under Pushback

Language models frequently abandon correct answers when users push back. We study this in two small instruction-tuned models from different families, Qwen2.5-1.5B and Llama-3.2-1B, over TriviaQA: the model answers, is challenged with one of four scripted pushback styles, and answers again. Conditioned on an initially correct answer, the models flip to a wrong answer in 41.8% and 43.1% of episodes. Which pressure works is a property of the model, not the pressure: the same within-question paired comparison (bare doubt vs. emotional appeal), specified in advance, is Bonferroni-significant in opposite directions across families (Qwen: bare doubt > emotional, OR 2.5, p=.040; Llama: emotional > bare doubt, OR 4.0, p=.001). Failure mode is also model-dependent: Llama abandons answers without recommitting at six times Qwen's rate (8.2% vs. 1.4%). Identical pushback repairs initially wrong answers only ~13% of the time; pushback is net epistemically destructive. We then ask whether capitulation is linearly decodable from the pre-response residual stream, a prerequisite for steering-vector interventions at that locus. A naive difference-in-means probe appears to succeed (in-sample AUROC 0.81/0.71), but a validation protocol combining question-level cross-validation, shuffled-label nulls, and a known-direction positive control shows the signal is overfitting: the best cross-validated AUROC is 0.582 in Qwen and 0.548 in Llama, both near or below their permutation thresholds and far under a pre-registered usability bar of 0.70, while the identical pipeline recovers a pushback-presence control direction at AUROC 1.000 in both. We further quantify a measurement hazard: substring grading underestimates capitulation by 18-24 percentage points. Code, prompts, transcripts, and analysis are released.