Characterizing When Multi-LLM Consensus Hides Hallucination with Response-Cloud Geometry

Multi-LLM systems increasingly treat agreement across independently queried models as a check against hallucination. Because frontier models share training corpora, their errors can correlate, so independent models may converge on the same falsehood, turning agreement into a false consensus. We introduce SiGMA (Spectral Geometry of Multi-model Agreement), which reads the spectral and volumetric geometry of the per-question response cloud rather than agreement magnitude. Nine commercial LLMs were queried once each on TruthfulQA, SimpleQA, and FreshQA, and each question’s nine embedded answers were binned into five consensus states by the number of wrong answers. Mean pairwise agreement reads almost identically at total failure on all three datasets and cannot separate convergent from dispersed error. The volumetric descriptors flip sign. On adversarial-misconception items the all-wrong (AW) cloud contracts until its mode-spread volume is statistically non-separable from correct consensus (p=0.91, n=27), whereas it expands on the other two benchmarks. A tightly contracted cloud can therefore accompany total failure, so high consensus is not evidence of correctness. An exploratory query-type router lowers TruthfulQA AW false-accepts from 44% to 33%. Because total failure is rare, this regime rests on a small sample and is read as high-risk rather than as a prevalence estimate.