Vector graphics rendering in low-level C demands deterministic graph traversal and flow computation to guarantee visual correctness and performance. We present a compact engine that models drawing primitives as a directed acyclic graph (DAG) and applies breadth-first search for rasterization while maintaining a residual network for dynamic path optimization. Formal invariants enforce acyclicity and optimal substructure, enabling incremental updates without recomputation. Static analysis of the source yields a worst-case traversal cost of O(|V|+|E|) and a flow relaxation cost of O((|V|+|E|)log |V|). No empirical timing 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_22_vector_graphics_in_lil,
title={Maximum Cardinality Invariants and Verification of Vector Graphics in Aether-Alpha...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-22_vector_graphics_in_lil/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-22_vector_graphics_in_lil/2026-10-22_vector_graphics_in_lil.pdf}}
}