A Geometric Instrument for Measuring Interrogative Entropy in Language Systems v.02

AbstractThis paper introduces a geometric measurement instrument for quantifying interrogative structure in language systems and establishes two major advancements in Version 2. First, we provide a formal mathematical framework and proof showing that interrogative entropy evolves deterministically under fixed question inputs. The proof demonstrates that interrogative classification, field dynamics, and entropy computation each behave as deterministic operations and therefore compose into reproducible entropy trajectories independent of stochastic answer generation. Second, we validate the instrument’s predictive utility through large-scale empirical analysis of the Anthropic HH-RLHF dataset ($n = 321{,}600$ prompt–response pairs). We show that user prompt interrogative structure predicts systematic differences in assistant response affect drift. Specifically, high-entropy (mixed WH-structure) prompts elicit approximately 25% more affect drift than low-entropy focused prompts, and certain interrogative dimensions (WHEN, WHO) consistently produce higher drift than others (HOW). New in Version 2 (December 2025) Formal proof – Mathematical demonstration that interrogative entropy is deterministic and separates question structure from model behavior. Empirical validation – Analysis of the Anthropic HH-RLHF dataset revealing that question geometry predicts affect drift (humanistic/hedging language). Software implementation – Open-source Python repositories for the $\Omega$-classifier and drift analysis tools. Software repositories Instrument: https://github.com/btisler-DS/CubeGeometryTest RLHF analysis pipeline: https://github.com/btisler-DS/h-drift-lab