Tethered Reasoning: Decoupling Entropy from Hallucination in Quantized LLMs via Manifold Steering

Quantized language models face a fundamental dilemma: low sampling temperatures yield repetitive, mode-collapsed outputs, while high temperatures (T > 2.0) cause trajectory divergence and semantic incoherence. We present HELIX, a geometric framework that decouples output entropy from hallucination by tethering hidden-state trajectories to a pre-computed truthfulness manifold. HELIX computes a Unified Truth Score (UTS) combining token-level semantic entropy with Mahalanobis distance from the manifold. When UTS indicates trajectory divergence, graduated steering vectors redirect activations toward structurally coherent regions while affecting only 0.2-2.5% of tokens. On 4-bit quantized Granite 4.0 H Small (32B/9B active, hybrid Mamba-Transformer): GSM8K maintains 88.84% accuracy at T = 3.0 (2.81pp degradation from T = 0.5); MMLU maintains 72.49% across 14,042 questions (1.24pp degradation). This demonstrates that high-temperature hallucination is primarily trajectory divergence rather than semantic collapse. Notably, steering the sparse Transformer attention layers (~10% of layers) is sufficient to correct drift in the Mamba-2 state-space formulation. Geometric tethering reveals a previously-masked High-Entropy Creative Reservoir. At T > 2.0, steered outputs exhibit 5-20% idea duplication versus 70-80% at conservative settings. Cross-architecture validation (Qwen3-30B-A3B MOE) confirms this phenomenon is architecture-independent, with 46.7% higher unique concept generation. HELIX acts as a syntax tether, enabling exploration of semantic diversity without violating the logical backbone required for valid output. This enables Multi-Temperature Synthesis, generating 200% more unique concepts than single-temperature inference.