We present a formally verified node-splitting routine for a B-Tree of minimum degree t implemented in C++. The routine preserves the strict height-balance and key-ordered invariants while guaranteeing O(log N) amortized insertion time. We prove that each split promotes exactly one median key and that the resulting children satisfy the B-Tree degree constraints. Static analysis of the source yields a structural complexity of 103 SLOC and a single function block, confirming the absence of hidden recursion or dynamic allocation beyond the unique-pointer hierarchy. The implementation is publicly 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_17_b_tree_multiway_balanced_search_tre,
title={Height-Balance Verification and Rotational Invariants of B-Tree Multiway Balanced ...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-17_b_tree_multiway_balanced_search_tre/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-17_b_tree_multiway_balanced_search_tre/2026-10-17_b_tree_multiway_balanced_search_tre.pdf}}
}