Dynamic package support in the Aether-Compiler introduces a dependency-aware resolution mechanism that must preserve structural invariants while maintaining logarithmic lookup performance. We embed a height-balanced binary search tree within the PackageRegistry to index package names, enabling O(log N) point and range queries for dependency resolution. The tree is augmented with a cycle-detection stack that guarantees acyclic dependency graphs. We prove that the tree remains strictly height-balanced after each insertion and rebalancing step, ensuring that the depth of the registry never exceeds ⌈ log₂ N ⌉ + 1. The implementation is fully expressed in Ruby, leveraging immutable package descriptors and lazy loading. No runtime benchmarks are reported; all evidence derives from static AST inspection and formal invariant proofs.
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_19_free_pascal_compiler_now_supports_d,
title={Height-Balanced Dependency Graphs in a Ruby Aether-Compiler Dynamic Package System},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-19_free_pascal_compiler_now_supports_d/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-19_free_pascal_compiler_now_supports_d/2026-10-19_free_pascal_compiler_now_supports_d.pdf}}
}