Static γ Modulation of Backbone Token-Mixer Outputs: 18% Reasoning-Stratum Perplexity Reduction Without Training

This paper documents a static inference-time modification that produces an 18.18% reduction in reasoning-stratum perplexity on dense transformer models without training or architectural changes. The mechanism applies a scalar amplification factor γ to the token-mixer output at each of a small set of middle transformer blocks. The intervention requires no gradient computation, adds negligible inference overhead (a scalar multiplication per amplified block per token), and preserves the model's own residual stream computation without additive injection. The mechanism has been tested across current-release (Q2 2026) Dense-class models including Gemma 4 E4B, Gemma 4 31B, Bonsai Ternary 8B, Qwen 3.5 4B, Qwen 3.5 8B, and Qwen 3.6 27B. This paper reports detailed measurements on Qwen 3.6 27B. At the canonical operating point (γ = 1.02), the mechanism produces an 18.18% reasoning-stratum perplexity reduction relative to unmodified baseline, with prose-stratum perplexity essentially unchanged (change of −0.09%) and code-stratum perplexity reduced by 17.52%. Empirical validation includes per-stratum perplexity measurements on the primary evaluation corpus, sensitivity analysis on an expanded structured-benchmark corpus, and coherence verification of generated outputs. Cross-substrate characterization is subject of future work. The mechanism is the subject of filed U.S. provisional patent applications. Commercial use requires a separate licensing agreement with the author. Please direct commercial licensing inquiries via https://lucasroot.com/contact.