Multi-stage LLM pipelines that perform multi-agent debate, intrinsic self-correction, or retrieval-augmented verification exhibit puzzling aggregate behaviors: accuracy plateaus and reversals across rounds, non-replication of debate gains on contemporary frontier models, intrinsic self-correction degradation, and qualitative cross-provider divergence in debate dynamics. Downstream agent response can be operationalized as two coupled decisions: detection (whether to treat upstream content as authoritative) and conditional generation (what to produce if not). This decomposition yields four observable response regimes, of which detection-without-correction is the load-bearing failure mode. Across a nine-cell empirical grid spanning four model families, four benchmarks (GSM8K, MATH-500, GPQA-Diamond, AIME), and two methods (multi-agent debate, intrinsic self-correction), we find that the conditional miscorrection rate is consistently dominant (53-94% across cohorts) while detection rate varies contextually by more than an order of magnitude. The framework unifies the four phenomena above as signatures of a common mechanism and characterizes detection threshold as a stable model/protocol-level regularity that persists across methods at matched benchmark difficulty.