Distributed task schedulers must guarantee timely execution, fault tolerance, and efficient resource utilization while operating over heterogeneous nodes. We present a height-balanced indexing mechanism that embeds job metadata, retry counters, lease expirations, and failure states into a single balanced search tree. The design preserves strict height-balance and key-order invariants, enabling deterministic O(log N) point and range queries for job allocation, lease renewal, and failure detection. Formal invariants are proven using a structural induction on the tree, and static analysis confirms that the C\# implementation satisfies the required O(log N) bounds without dynamic memory fragmentation. No empirical wall-clock measurements are reported; all evidence derives from AST inspection and invariant proofs.
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_15_distributed_task_scheduler_system_d,
title={Height-Balanced Indexing for Distributed Task Scheduling: Jobs, Retries, Leases, a...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-15_distributed_task_scheduler_system_d/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-15_distributed_task_scheduler_system_d/2026-10-15_distributed_task_scheduler_system_d.pdf}}
}