System Prompt Framing Induces Attention-Dependent Entropy Regime Switching in Transformer Token Generation

We present a systematic study of how system prompt framing modulates token-level Shannon entropy

during language model inference. Across three experimental phases totaling 3,830 inference runs, we

orthogonalize two prompt factors—relational presence (R), which frames generation as collaborative

inquiry, and epistemic openness (E), which licenses uncertainty and exploration—and measure their

individual and joint effects on next-token probability distributions. Phase 1 (900 runs across 6 models at 3

parameter scales) establishes that the co-creative condition (R+E+) produces elevated entropy relative

to controls, with effect sizes scaling from negligible at 0.5B parameters (d= 0.13, NS) to large at 7B+

(d>1.0) across four architectures. Phase 2 (2,000 runs, 8 conditions, 5 architectures) decomposes the

effect via a 2×2 factorial: the R×E interaction is superadditive on two of three responsive transformers

(+0.19, +0.21) but absent in a pure state-space model (Falcon3-Mamba-7B;−0.04), consistent with

the hypothesis that cross-factor binding requires the attention mechanism. Appending safety constraint

language to the co-creative frame suppresses the effect on transformers (d = 0.85–1.22) but not on

the SSM (d = 0.22, NS). Phase 3 (930 runs, 5-factor response surface) confirms agonist-antagonist

classifications on a single model. Baseline and analytical controls are statistically indistinguishable across

all architectures (d<0.10). We release all data, code, and prompts.