We present Chronos-Trace, a lightweight graph-centric engine that reconstructs the causal chain of a food-borne outbreak by traversing a supply-chain dependency graph. The algorithm performs a depth-first search augmented with a priority-based relaxation to identify all minimal source nodes that could have introduced the contaminant. We formally prove that the traversal preserves acyclicity and that the relaxation yields an optimal substructure invariant. Static analysis of the C\# implementation yields a worst-case time bound of O(|V|+|E|)+O((|V|+|E|)log |V|) and linear auxiliary memory. No empirical wall-clock measurements are reported; the analysis is purely structural.
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_25_forktrace_following_a_food_outbreak,
title={Chronos-Trace: Graph-Based Back-Tracing of Food Outbreaks in C#},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Agentic Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-25_forktrace_following_a_food_outbreak/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-25_forktrace_following_a_food_outbreak/2026-10-25_forktrace_following_a_food_outbreak.pdf}}
}