Zeng, Xiaozhou: Graph-Theoretic Formalization of the Determination Dependency Graph: A Mathematical Foundation Aligned with Structural Determination Theory v5.9

This document develops a strict graph-theoretic formalization of the determination dependency graph G_D introduced in natural language in Structural Determination Theory (SDT) v5.9. Working at the level of partial-order theory, lattice theory, and elementary category theory, the formalization elevates SDT's core structural objects — nodes, edges, products, layers, traces — to a precisely defined four-tuple G_D = (V, →, ρ, λ). Principal contributions include: (i) formal proof of SDT's three core