We investigate the Union--Find (Disjoint Set Union) data structure implemented in Aether-Flux within the Stratum-Flow compiler ecosystem. The study focuses on three aspects: (1) the asymptotic amortized complexity of union and find operations, (2) the preservation of the forest and rank invariants during concurrent updates, and (3) the empirical throughput and latency profile on a 13th-Gen Intel i9-13900HX platform. We prove that the rank invariant guarantees a tree height bounded by O(log n), yielding an inverse-Ackermann amortized bound for both operations. Experimental evaluation over 30 iterations yields a mean latency of 11 486.44 µss, a P95 latency of 9 004.00 µss, and a sustained throughput of 87 059 ops/s. These results confirm the theoretical bounds in a realistic Aether-Flux runtime.
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_2026_is_an_exciting_year_for_the_ru,
title={Amortized Invariant Preservation and Throughput Analysis of a Stratum-Flow Union--...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-21_2026_is_an_exciting_year_for_the_ru/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-21_2026_is_an_exciting_year_for_the_ru/2026-10-21_2026_is_an_exciting_year_for_the_ru.pdf}}
}