BiAxisAudit: A Novel Framework to Evaluate LLM Bias Across Prompt Sensitivity and Response-Layer Divergence

Bias audits of large language models now operate within governance frameworks such as the EU AI Act, making benchmark reliability a security concern in its own right. Many current benchmarks, however, collapse bias into a single scalar from one prompt format and one surface label. This design misses two failure modes that can be exploited without changing model weights. Across prompts, meaning-preserving format changes shift bias endorsement by more than $0.7$ on a fixed statement pool. Within a response, the discrete Selection and free-text Elaboration can take opposing stances, so an apparently clean aggregate may hide substantial internal inconsistency (a ``cancellation trap''). Selection-only and elaboration-only rankings are therefore nearly uncorrelated across eight LLMs (Spearman $ρ= 0.238$, $p = 0.570$): LLaMA3-70B ranks in the middle under selection-only scoring but highest under elaboration-only scoring on the same responses. We introduce \textsc{BiAxisAudit}, a protocol that reports each bias score together with a reliability estimate on two orthogonal axes. The across-prompt axis evaluates each statement under a factorial grid of task format, perspective, role, and sentiment, treating bias as a distribution rather than a point estimate. The within-response axis uses Split Coding to recover Selection and Elaboration as separate signals, measured by the Inconsistency Rate and Divergence Net Imbalance. Across eight LLMs with $80{,}200$ coded responses each, task format alone explains as much variance as model choice; $63.6\%$ of pooled bias signals (up to $85.2\%$ per model) appear in only one coding layer, and prompt-dimension interactions exceed main effects. The instrument also separates real bias reductions from apparent reductions caused by cross-layer redistribution: some prompt configurations reduce both BER and IR, whereas others suppress only selection-layer bias.