We report fundamental insights into how agentic graph reasoning systems spontaneously evolve toward a critical state that sustains continuous semantic discovery. By rigorously analyzing structural (Von Neumann graph entropy) and semantic (embedding) entropy, we identify a subtle yet robust regime in which semantic entropy persistently dominates over structural entropy. This interplay is quantified by a dimensionless Critical Discovery Parameter that stabilizes at a small negative value, indicating a consistent excess of semantic entropy. Empirically, we observe a stable fraction (12%) of "surprising" edges, links between semantically distant concepts, providing evidence of long-range or cross-domain connections that drive continuous innovation. Concomitantly, the system exhibits scale-free and small-world topological features, alongside a negative cross-correlation between structural and semantic measures, reinforcing the analogy to self-organized criticality. These results establish clear parallels with critical phenomena in physical, biological, and cognitive complex systems, revealing an entropy-based principle governing adaptability and continuous innovation. Crucially, semantic richness emerges as the underlying driver of sustained exploration, despite not being explicitly used by the reasoning process. Our findings provide interdisciplinary insights and practical strategies for engineering intelligent systems with intrinsic capacities for long-term discovery and adaptation, and offer insights into how model training strategies can be developed that reinforce critical discovery.

本研究解决了代理图推理系统在持续语义发现过程中自发演变至临界状态的机制缺口。通过分析结构熵和语义熵的交互，提出了一种新的临界发现参数，表明语义熵在系统中占主导地位。研究发现系统中存在12%的“惊奇”边，表明概念之间的远程连接，这一发现为智能系统设计提供了跨学科的见解和实践策略，以促进长期发现与适应。

自组织图推理演变为持续发现的临界状态：通过结构-语义动态