Memory Economics in Generational Artificial Life: How Environmental Volatility Dictates the Phase Boundary Between Lamarckian Inheritance and Agile Amnesia

In evolutionary computation, cultural evolution, and continual machine learning, lineages face a fundamental tension between retaining ancestral knowledge (stability) and acquiring novel skills (plasticity). While exact "Lamarckian" parameter transfer accelerates adaptation in static environments, real biological and cultural lineages operate under strict metabolic budgets and non-stationary conditions. In this unified treatise, we formalize the theory of Memory Economics: 1. The Capacity-Saturation Trap: When agent memory capacity is strictly bounded, exact cloning causes catastrophic failure under environmental volatility (p < 10^-5), establishing lossy transmission as an indispensable mathematical regularizer. 2. Memory Economics Phase Diagram: By allowing retention (f), learning rate (lr), and memory capacity (c) to co-evolve under metabolic costs, we map a distinct non-monotonic phase diagram across shift timescales (N=30 independent runs per regime, Welch's t = 30.925, p = 2.86e-32, Cohen's d = 7.98, SHA-256 verified). Rapid volatility produces a "boomerang" strategy; intermediate volatility forces "agile amnesia" where 85.6% of active memory is newly learned; stable eras foster "Lamarckian rentiers." 3. Neural Continual Learning: We demonstrate that this phase boundary translates directly to deep neural network agents (MLPs) undergoing continual classification on non-stationary, alternating task boundaries.