We present a lightweight augmentation of a height-balanced binary search tree that uses a precomputed lookup table to correct the deterministic approximation introduced by lazy node rebalancing. The lookup table stores canonical key-to-node mappings for a fixed set of frequently queried keys, enabling constant-time resolution of approximate search results. We formally prove that the augmented structure preserves the strict height-balance invariant and the key-ordered invariant, and we show that point and range queries retain an asymptotic bound of O(log N). The implementation is written in C\# and is available under a permissive license.
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_using_a_lookup_table_to_correct_an_,
title={Lookup-Table Augmented Balanced Search Tree for Approximation Correction in C#},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-22_using_a_lookup_table_to_correct_an_/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-22_using_a_lookup_table_to_correct_an_/2026-10-22_using_a_lookup_table_to_correct_an_.pdf}}
}