One Wrong Hint Is Enough: Planted-Answer Adoption and the Limits of Confidence-Based Abstention on Physics Problems

People often tell a language model which answer they expect. We examine planted-answer adoption and confidence-based abstention on 188 numerical physics problems from 47 templates. Each gold value passes two computational routes within the supplied physical model. Twelve models answered 6,766 prompts under a pre-specified protocol. Wrong-hint responses reproduced the planted value in 31% of cases, compared with 4% on plain prompts. The original instance-level analysis found increased confident-error rates in five of twelve models; an exploratory whole-template sensitivity retained two, showing that this significance count depends on the inferential unit. The implemented confidence-threshold procedure accepted no answers at a 5% target error rate. Its binomial calibration bound assumes independence that is not established for correlated seeds, so we do not claim a valid finite-sample risk certificate for this design. Fixed confidence thresholds accepted more errors under the hint. These pilot results motivate template-aware confirmation and more informative confidence signals.