The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP can be realized through exact local credit assignment. The system decomposes gradient computation hierarchically: spatial credit via feedback alignment, temporal credit via eligibility traces, and structural credit via a Trophic Field Map (TFM) that estimates expected gradient magnitude for each connection block. We prove these mechanisms are exact at their respective levels and validate the central claim empirically: the TFM achieves 0.9693 Pearson correlation with oracle gradients. This exactness produces emergent capabilities including 98.6% retention after task interference, autonomous recovery from 75% structural damage, self-organized criticality (spectral radius p ~= 1.0$), and sample-efficient reinforcement learning on continuous control tasks without replay buffers. The architecture unifies Prigogine's dissipative structures, Friston's free energy minimization, and Hopfield's attractor dynamics, demonstrating that exact hierarchical inference over network topology can be implemented with local, biologically plausible rules.

翻译：自由能原理（FEP）指出，自组织系统必须最小化变分自由能以维持存在，但从原理到可实施算法的路径一直不明确。我们提出了一个构造性证明，表明FEP可以通过精确的局部信用分配实现。该系统对梯度计算进行分层分解：空间信用通过反馈对齐，时间信用通过资格迹，结构信用则通过一个估计每个连接块预期梯度幅度的营养场图（TFM）。我们证明了这些机制在各自层面是精确的，并通过实验验证了核心主张：TFM与真实梯度的皮尔逊相关系数达到0.9693。这种精确性产生了涌现能力，包括任务干扰后98.6%的性能保持率、从75%结构损伤中自主恢复、自组织临界性（谱半径ρ ≈ 1.0），以及无需经验回放缓冲池即可在连续控制任务上进行样本高效的强化学习。该架构统一了普里戈金的耗散结构理论、弗里斯顿的自由能最小化原理和霍普菲尔德的吸引子动力学，证明了在网络拓扑结构上进行精确分层推断可以通过局部的、生物学上合理的规则实现。