We present a lightweight, mode-aware path engine implemented in Zig that computes shortest multimodal routes on a 228,060-edge urban graph. The engine augments a standard adjacency array with a mode tag and applies Dijkstra's algorithm restricted to user-supplied mode sets. We formally prove that the returned path satisfies the optimal substructure invariant and that the algorithm runs in O(|V|+|E|) for traversal and O((|V|+|E|)log |V|) for relaxation. Static analysis of the source yields 164 SLOC and eight function blocks, confirming the modest code footprint. No empirical runtime measurements are reported; all claims are supported by formal proofs and AST inspection.
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_18_engineering_a_multimodal_travel_pla,
title={Optimal Substructure Invariants in a Zig-Based Multimodal Travel Planner for a 228...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-18_engineering_a_multimodal_travel_pla/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-18_engineering_a_multimodal_travel_pla/2026-10-18_engineering_a_multimodal_travel_pla.pdf}}
}