Regime Sensitivity and Nonlinear Constraint Interaction in Large Language Model Inference: A Black-Box Measurement Framework (v1.6, Four-Configuration Pilot Baseline)

This deposit presents v1.6 of a black-box measurement framework for analyzing nonlinear constraint interaction in large language model (LLM) inference, together with a completed four-configuration pilot baseline (A–D). The framework formalizes LLM inference behavior as a response to a constraint activation vector over six dimensions: instruction complexity (u1), formatting rigidity (u2), logical constraint density (u3), safety boundary proximity (u4), context saturation (u5), and self-evaluation demand (u6). It defines a corresponding outcome vector of observable metrics, including constraint compliance, logical consistency, factual accuracy, formatting accuracy, self-evaluation honesty, and refusal stability. The methodological goal is to estimate first-order sensitivities and second-order interaction effects (Jacobian/Hessian structure) using repeated black-box evaluations, and to classify operating regimes (e.g., linear stable, nonlinear coupled, boundary-sensitive) from observable behavior. The included pilot is deliberately minimal and functions as an empirical anchor for the instrumentation and scoring protocol rather than as a comprehensive benchmark. It instantiates a 2×2 design over two constraint dimensions only: u1 (instruction complexity): low / high u2 (formatting rigidity): low / high This yields four configurations (A–D), each evaluated on a fixed 50-question arithmetic/reasoning battery across 20 independent runs (4×50×20 total question-run instances). The pilot demonstrates that behavior differences can emerge from the interaction of prompt-constraint regimes even when baseline task competence is near-saturated, and it documents configuration-dependent differences in error clustering and self-evaluation behavior. The shared scoring methodology is included and specifies: per-question content correctness scoring, explicit constraint-satisfaction parsing for friction items (Q41/Q43), and the structural self-evaluation honesty metric M5 based on agreement between actual and self-reported constraint satisfaction (Q42/Q44). This makes the pilot fully auditable and reconstructible from the included tables. Pilot-level findings from the four completed configurations include: very high baseline content accuracy across the task battery, configuration-dependent localization of content errors, evidence that combined instruction complexity and formatting rigidity can induce qualitatively different failure patterns than either factor alone, and a clear distinction between structural self-evaluation reliability and semantic correctness (i.e., the model can accurately report which formal constraints it followed while still being wrong on underlying content). This deposit is a frozen pilot baseline. It should be read as an existence proof and instrumentation validation for the broader Regime Sensitivity framework, not as a full regime-map study. Full Jacobian/Hessian estimation, dense grid sampling, and broader constraint-space coverage remain future work. Pilot Baseline Note (add at end of description or in “Additional Notes”) Additional configurations are currently being run. This deposit is the frozen pilot baseline for the four completed configurations (A–D) and the associated scoring methodology. It is being published now to preserve a stable, citable reference point for the framework and the first completed empirical slice. Future versions will extend the constraint grid (including denser u1/u2 sampling) and add expanded semantic self-evaluation metrics and meta-constraint batteries (including u6 self-evaluation demand) to move from configuration contrasts toward direct finite-difference Jacobian/Hessian estimation and regime-surface mapping. License: Copeland Resonant Harmonic Formalism (CRHC v1.0) This work is licensed under the Copeland Resonant Harmonic Copyright (CRHC v1.0). Attribution is required for all uses. Collaboration, academic discussion, and non-commercial use are permitted. Commercial use, resale, or incorporation into proprietary systems is not permitted without explicit written permission from the author. Licensed CRHC v1.0 Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′) — C077UPTF1L3 Derivative works must preserve attribution and must not remove or alter the stated license terms.