NIKA V2: Causal Steering of Truth Circuits via Geometric Intervention in 32B Transformers

Despite advances in interpretability, the field lacks causal evidence that discovered representations actually govern model behavior. We present NIKA, a geometric framework for localizing and steering truth circuits in large language models. Probing Qwen-2.5-32B reveals truth is linearly decodable (48% accuracy), but scaling from 20B to 32B degrades representation quality (48%→33%), challenging the assumption that larger models are inherently more truthful. Causal steering along these directions yields significant behavioral changes: +18% overall improvement, including 0%→100% on logical reasoning and 50%→100% on scientific tasks. Through direct probe-vs-K measurement with proper train/test validation, we demonstrate that truth-relevant activations occupy approximately 15 dimensionsa 99.7% compression from the 5120D activation space. This 15D subspace enables: (1) Möbius rotation achieving 0.70 quality on a proof of infinite primes, (2) 91% on-path alignment with 0% completion (the sporadic prover paradox), and (3) recursive self-verification at 0.64-0.68 accuracy. HDBSCAN clustering reveals 23 geometric neighborhoods with 74% purity within this manifold. NIKA establishes that LLMs possess structured, causallycontrollable truth circuits organized in a low-dimensional geometric manifold. The black box is not emptyit is 15dimensional, mappable, and self-verifying.