C3: Long-Horizon Character Consistency via Causal-Continuous State Dynamics and Memory Rewriting

Maintaining character consistency over long-horizon gameplay is a critical bottleneck for deploying Large Language Models (LLMs) as Non-Player Characters. Prevalent discrete Affective State Machines (ASMs) fail due to two paradoxes: (1) the \textit{Cliff-edge Effect}, where threshold-based switching causes jarring narrative discontinuities; and (2) \textit{Auto-regressive Inertia}, where accumulated dialogue history dilutes current state instructions. We propose \textbf{C3 (Causal-Continuous Characterization)}, which couples a continuous state space with \textit{hysteresis-aware dynamics} to dampen emotional volatility, and a \textit{State-Conditioned Memory Rewriting} mechanism that re-contextualizes past events through the lens of the current relationship. On a 100-turn dynamic simulation (\textsc{Chronos-Sim}, 5{,}000 turns per condition), C3 achieves a \textbf{10.5\% absolute SAR improvement} over a strong smoothed-ASM baseline (Welch's $t$-test, $p < 0.0001$, Cohen's $d \approx 3.97$). Cross-model evaluations on \texttt{Llama-3-8B-Instruct} and \texttt{Mistral-v0.2-7B} reproduce the relative gain, indicating the mechanism transfers across backbones although absolute SAR remains backbone-dependent. A human study with 20 game designers (ICC$=0.74$) corroborates higher perceived consistency, and a separate factual audit (Fleiss' $\kappa=0.81$) confirms the Rewriter alters interpretation without corrupting facts. Deployment analysis shows a $\sim$60\% reduction in long-session token consumption.