We present CaRPS, our system for Track 1 of StanceEval-2026. CaRPS combines a target-conditioned encoder with an LLM-based labeling and verification process to handle targets that are not seen during encoder fine-tuning. The encoder takes both the target and the tweet as input, while the LLM is used to generate labels and verify difficult predictions. These LLM-generated labels can then be used as pseudo-labeled data to further fine-tune the encoder, with the goal of gradually reducing the need for LLM calls. On the development leaderboard, our target-conditioned encoder alone achieves 87.19% Favg2, 76.56% Favg3, and 85.30% accuracy. For the official evaluation, we used adversarial LLM prompting for the target not seen during encoder fine-tuning, achieving 82.89% Favg2, 62.67% Favg3, and 78.98% accuracy. Additional experiments show that adversarial verification improves stance and sarcasm classification over one-shot prompting, while pseudo-label self-training helps adapt the encoder to a held-out target. Overall, CaRPS explores a practical combination of efficient encoder-based prediction and LLM-based labeling and verification for Arabic stance detection.