Supporting Formal Specifications, Verification Artifacts, and Reproducibility Materials for Traversal-Governed Full-Stack Development for Hierarchical Systems

This appendix provides supporting formal specifications, verification artifacts, empirical protocols, and reproducibility materials for the manuscript “Traversal-Governed Full-Stack Development for Hierarchical Systems: Formal Semantics, Verification, and Longitudinal Evaluation.” It contains formal notation and semantic definitions; state-machine and CSPM specifications for Directed Acyclic Development (DAD), Depth-First Development (DFD), Breadth-First Development (BFD), Cyclic Directed Development (CDD), Primary Depth-First Development (PDFD), and Primary Breadth-First Development (PBFD); formal specifications and complexity analysis for Three-Level Encapsulation (TLE); theorem proofs and verification artifacts; MVP implementation materials; empirical protocols and supporting analyses; and an artifact provenance registry. The appendix is provided as a technical reference and reproducibility supplement to the self-contained main manuscript. Version-controlled research artifacts referenced by the appendix are documented through the provenance registry in Appendix A.22.