Modern deep learning workloads require complex multidimensional tensor manipulations on GPU architectures. This paper formalizes a simplified layout algebra for GPU kernels, proving height-balance and bijective dimension mapping invariants.
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_a_simplified_layout_algebra_for_gpu,
title={Huge Inductive Invariant Proofs and State Space Limits in A Simplified Layout Alge...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-13_a_simplified_layout_algebra_for_gpu/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-13_a_simplified_layout_algebra_for_gpu/2026-10-13_a_simplified_layout_algebra_for_gpu.pdf}}
}