Bootstrapping a compiler entails repeatedly parsing, interpreting, and compiling source fragments until a self-hosting binary is produced. While the functional correctness of each phase is well studied, the underlying data-structural mechanisms that guarantee deterministic progress are less understood. This paper examines a balanced search and indexing structure implemented in Go that underpins symbol table management during bootstrapping. We formalize the height-balanced and key-ordered invariants, derive an amortized logarithmic bound for insertion and lookup, and verify these properties through static abstract-syntax-tree (AST) inspection. The analysis confirms that the structure scales as O(log N) for point and range queries and requires linear auxiliary memory. No empirical wall-clock measurements are reported; all evidence is derived from formal reasoning and structural profiling.
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_14_compiler_bootstrapping_depends_on_m,
title={Causal Order Preservation and Height-Balanced Indexing in a Go Compiler Bootstrapp...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-14_compiler_bootstrapping_depends_on_m/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-14_compiler_bootstrapping_depends_on_m/2026-10-14_compiler_bootstrapping_depends_on_m.pdf}}
}