"Don't Fall Behind": A Unified Framework of Dynastic Survival, Two-Stage Belief Error, and the Modern Involution Trap

We set out to solve a dual puzzle regarding reproductive strategies: The "Ancient vs. Modern" Puzzle (why pre-modern elites adopted a "Survival" strategy while modern elites adopt an "Anxiety" strategy) and the "Class Divide" Puzzle (why modern involution manifests as a U-shaped fertility pattern). We develop a unified computational framework (DP + Monte Carlo) that introduces Cognitive Heterogeneity across classes. Our Hybrid Model (M-H) posits that the poor act as "Rational Survivors" (M1 utility, Reality parameters), while the middle/rich act as "Biased Strivers" (M4b utility, Belief parameters). Our simulations yield three core findings. First, we confirm that the "Survival" strategy is objectively rational whenever risk exceeds a low threshold ($\sigma > 0.45$). Given that real-world risk is massive ($\sigma_{Real} \approx 4.9$), the modern "Quality" strategy is objectively fragile. Second, the trap for the Middle/Rich ($B \ge 200$) is driven by a "Two-Stage Belief Error": they are first "baited" by a Causal Error (underestimating risk) to enter the status game, and then "trapped" by a Marginal Error (underestimating returns) which triggers a stop in fertility. Third, the U-shape is driven by the cognitive divide. The Poor escape the trap by retaining a "Rational Survival" strategy in the face of real high risk. Conversely, the Aspirational Middle Class ($HC \approx 12, B \ge 200$) is uniquely trapped by their Biased Beliefs. Their high competence raises their dynastic reference point ($R$) to a level where, under perceived low returns, restricting fertility to $N=1$ becomes the only rational choice within their biased belief system.