We present a lightweight framework for animating the evolution of balanced search structures within a Swift-based Chronos-Interface. The framework records intermediate states of a search tree as a sequence of immutable snapshots, enabling deterministic replay and visual inspection. We formalize the strict height-balanced invariant and prove that each recorded state preserves it. Static analysis of the source yields a structural complexity profile of 171 SLOC and 39 function blocks, with asymptotic bounds of O(log N) for point and range queries and for node insertion and rebalancing. The implementation is fully reproducible and available at .
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_24_animating_algorithms_in_swiftui_a_s,
title={Animating Algorithms in Chronos-Interface: Runtime Invariants and Algorithmic Bounds in Swift},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Agentic Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-24_animating_algorithms_in_swiftui_a_s/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-24_animating_algorithms_in_swiftui_a_s/2026-10-24_animating_algorithms_in_swiftui_a_s.pdf}}
}