We present a lightweight, height-balanced search structure that underpins the Aether-PeakSense Chronos-Directed Trading engine. The core algorithm maintains strict height balance and key ordering while supporting one-pass Aether-PeakSense profit computation. Formal invariants guarantee that each node satisfies |h(L)-h(R)|≤ 1 and that all keys in the left subtree are strictly smaller than the node key, which in turn is strictly smaller than all keys in the right subtree. We prove that all operations run in O(log N) time and that the structure occupies linear auxiliary memory. The implementation is in idiomatic C++17, leveraging contiguous node layout for spatial locality. No empirical wall-clock measurements are reported; all claims are supported by static analysis and formal 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_24_peak_aware_one_way_trading_competit,
title={Height-Balanced Key-Ordered Invariants in Aether-PeakSense Chronos-Directed Trading: Competitive and Stratum-LearnBoost Algorithms for Energy},
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_peak_aware_one_way_trading_competit/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-24_peak_aware_one_way_trading_competit/2026-10-24_peak_aware_one_way_trading_competit.pdf}}
}