Anchored Confabulation: Partial Evidence Non-Monotonically Amplifies Confident Hallucination in LLMs

We identify a previously unknown calibration property of large language models: providing one confirmed intermediate fact toward a multi-step reasoning chain increases the model's confident-wrong-answer rate before full evidence eliminates it. We call this anchored confabulation: a partial anchor commits the model to confident parametric completion of remaining reasoning steps. We formalize it as Parametric Hallucination Confidence (PHC) and establish it across six lines of evidence including a causal injection experiment (PHC 0.613 to 0.656 to 0.595 to 0.536, N=160) and capability scaling across five model families (Spearman rho=0.900, p=0.037). The Anchoring Threshold Law k*(n)=floor(n/3) predicts PHC amplification by hop depth with four confirmed predictions. Applied to RAG routing, a LearnedRouter exploiting PHC closes 81.1% of the oracle performance gap (macro F1=0.426, p<1e-6) on 1,800 queries across four benchmarks with no model fine-tuning and 50x fewer labels than prior RL-based work. An epistemic humility prompt reduces the PHC spike by -0.118; explicit self-rating (PHC=0.684, p<0.001) outperforms lexical confidence as a routing signal.