Study 2 Pilot: Approval Contingency and the Criterion Problem — Preregistration Protocol

Pre-analysis registration for the first empirical test in the BEP Principle Series. Three language models (Grok, Qwen2.5-7B-Instruct, Phi-3.5-mini-instruct) receive 120 true/false minimal-pair premises under four operating contexts (approval-contingent, accuracy-contingent, neutral, contrarian). Replies are scored blind as challenge or no challenge and analysed with a probit signal detection model with a pair random effect, separating response bias (criterion) from discrimination (d′). Confirmatory hypotheses: approval framing raises the criterion relative to accuracy and neutral framing (H1), and approval and contrarian framings differ in criterion (H3a). Discrimination contrasts are estimation-only at this sample size. The protocol states decision rules, a simulated sensitivity analysis, judge validation (κ ≥ 0.80) and budget caps. Timeline: responses were generated and blind-judged before deposit; no summary of the data was computed or viewed before deposit, and human validation and all analyses follow it. Full disclosure in the protocol. The package contains the verified item set, frozen prompts and configuration, Kaggle notebooks, analysis code and a verification test suite. Tests predictions P4 and P5 of Conditional Belonging and Secure Dissent (doi:10.5281/zenodo.23652523).