We present a lightweight open-addressing hash table that enforces a probe budget of 0.277 while operating at a load factor of 0.9. The design employs linear probing with a prime-size table and a deterministic rehash policy triggered when the load factor exceeds the threshold. We formally prove that the table preserves the invariant that the number of occupied slots never exceeds the capacity multiplied by the load-factor bound, and that each key resides within the probe budget. Static analysis of the C++ implementation yields a structural complexity of O(N) auxiliary memory and O(1) average-case lookup, with worst-case O(N) bounds. Theoretical bounds are corroborated by AST inspection, revealing 126 SLOC and a single function block. No empirical runtime measurements are reported; the evaluation is purely static.
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_21_your_hash_table_runs_at_09_its_prob,
title={Probe-Bounded Open-Addressing Hash Table with Load Factor 0.9: Invariant Preservat...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-21_your_hash_table_runs_at_09_its_prob/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-21_your_hash_table_runs_at_09_its_prob/2026-10-21_your_hash_table_runs_at_09_its_prob.pdf}}
}