Least Recently Used (LRU) caches are ubiquitous in systems that require bounded memory footprints. This work presents a formally verified TypeScript implementation that couples a hash map with a doubly linked list to achieve constant-time access, insertion, and deletion. We establish a precise invariant that the list order always reflects recency of use, and we prove that the invariant is preserved under all public operations. The algorithmic complexity is shown to be O(1) per operation, while the static abstract syntax tree (AST) analysis confirms a structural complexity of O(N) auxiliary memory and a balanced search-style insertion cost of O(log N).
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_least_recently_used_lru_cache_with_,
title={Inductive Invariant Proofs and State Space Limits in Least Recently Used (LRU) Cac...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-16_least_recently_used_lru_cache_with_/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-16_least_recently_used_lru_cache_with_/2026-10-16_least_recently_used_lru_cache_with_.pdf}}
}