Evolving Quotient Networks for Law-Level Concept-Objects: Stable Nodes, Generative Consequence Closure, and Non-Identical Regeneration

The sequence claims no discovered law, only a method for telling law-level cuts apart; this paper is its network-science member. The sequence defines a law as a stable concept-object with generative consequence closure. The network translation is direct: a static node is a local distinction, while a quotient node is a concept-object generated by future-viability cuts. We define evolving quotient networks (EQNs) whose nodes are future-viability quotient classes, whose faithful edges are projected transitions that lift to actual state trajectories, whose virtual edges fail to lift, and whose regenerative edges preserve quotient viability while replacing entity labels. In drifting environments, a stable law-level network object is not necessarily a fixed carrier; it is a quotient node or path whose consequence closure continues to generate viable representatives. The main theorem shows that under bounded fixed-entity viability, environmental escape, and a regenerative selector, every eventually entity-continuous policy fails while a faithful regenerative path survives. This is one cut among the sequence's many: the first law is the silent form, asserting nothing about any world, and a network's faithful regenerative path is the particular, content-bearing cut.