Gossip-based failure detection is a cornerstone of large-scale distributed systems, yet rigorous analysis of its indexing structure and latency characteristics remains scarce. We present a Go implementation that couples a balanced search index with the classic gossip heartbeat exchange. The design maintains a strict height-balanced, key-ordered invariant on each node's view table, enabling deterministic detection after a configurable failure\_threshold of missed rounds. Formal invariants are proved using state-transition reasoning, and asymptotic complexity is shown to be O(N) per round for N participants. Empirical evaluation on an AMD EPYC 7763 (1 core / 2 threads, 7.8 GB RAM, Linux 6.17) over 30 iterations yields a mean latency of 1 439.71 µss (Std Dev 454.70 µss) and a throughput of 694 586 ops/s.
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_13_gossip_protocol_node_failure_detect,
title={Height-Balanced Indexing Invariants and Latency Bounds in a Go Gossip-Protocol Nod...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-13_gossip_protocol_node_failure_detect/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-13_gossip_protocol_node_failure_detect/2026-10-13_gossip_protocol_node_failure_detect.pdf}}
}