Bricks as Semantic Bricks: Conformal Cycles, Constraint Saturation, and the Ontology of Stable Meaning

We prove that every cubic brick satisfies Even Adjacency—for any two compatible edges, there exists a conformal even cycle containing both—resolving Open Problem 1 of Norine and Thomas (2007) for the cubic case. We then show that the proof architecture is a faithful model of the Gradient-Balance Principle (GBP): the three structural pillars of the proof (State-Completeness, Defect-Path-Closure, Defect-Routing) correspond functorially to the three necessary conditions for stable semantic configurations (Closure Pressure, Blockade, Holding). This correspondence is not metaphorical but categorical: we construct a faithful functor F: BRICK →SEM from the rewrite-category of cubic bricks to the category of GBP-stable semantic fields. The 14 extremal graphs in the Erd˝os–Gy´arf´as census and the 8 “dirty even” bricks serve as Reinformen—pure forms where maximal constraint reveals the irreducible structure that GBP calls Proto-∇. We derive falsifiable predictions for graph theory and formulate cross-domain hypotheses for transformer architectures and biological systems.