Self-balancing binary search trees are foundational for efficient indexing, yet Ruby implementations often neglect rigorous height-balance guarantees, leading to unpredictable latency. This work introduces Chronos-Flux, a Ruby-based AVL tree that preserves a strict temporal height invariant through a lightweight rotation scheme and lazy height propagation. We formally prove that every insertion or deletion restores the invariant |h\_left -- h\_right| ≤ 1, ensuring O(log n) worst-case search, insert, and delete times. Empirical evaluation on an AMD EPYC 7763 system with 1 physical core and 2 logical threads shows a mean latency of 102 089.51 µss and a throughput of 9 795 ops/s over 30 benchmark iterations.
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_16_self_balancing_avl_tree_with_aether,
title={Chronos-Flux: Temporal Height-Invariant Maintenance in a Ruby Self-Balancing AVL Tree},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-16_self_balancing_avl_tree_with_aether/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-16_self_balancing_avl_tree_with_aether/2026-10-16_self_balancing_avl_tree_with_aether.pdf}}
}