Higher-Rank Completion Holonomy: Displacement-Marked Optimal Fibers and Physical LIFO Transport

This paper develops a higher-rank theory connecting the structure of optimal completion fibers with their physical realization in deterministic pushdown systems. The central idea is to retain not only the loop structure of the completion space but also the displacement information carried by those loops, allowing zero-displacement behavior to be distinguished from ordinary movement in the completion lattice. Using tools from periodic quotient topology, fundamental groups, finite permutation representations, combinatorial counting, and LIFO locality analysis, the paper derives exact laws for several rank-raising operations and explains how intrinsic completion structure transfers to physically realized transport, stack carrier requirements, ancestry locality, transient memory, and repair cost once a transport category is fixed. An explicit family valid in every active rank shows that finite transport complexity can remain constant while the required literal carrier height grows linearly, demonstrating that semantic rank, transport complexity, locality cost, and arithmetic carrier size are genuinely different quantities. The novelty lies not in the classical ingredients individually, but in combining them into a completion-specific framework with exact structural and resource theorems linking higher-rank completion geometry to concrete pushdown transport.