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 Cliff-edge Effect, where threshold-based switching causes jarring narrative discontinuities; and (2) Auto-regressive Inertia, where accumulated dialogue history dilutes current state instructions. We propose C3 (Causal-Continuous Characterization), which couples a continuous state space with hysteresis-aware dynamics to dampen emotional volatility, and a State-Conditioned Memory Rewriting mechanism that re-contextualizes past events through the lens of the current relationship. On a 100-turn dynamic simulation (Chronos-Sim, 5,000 turns per condition), C3 achieves a 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 Llama-3-8B-Instruct and 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.