Computational Audit and Adaptive Regularization of Fractal Matrix Constructions in OpenAI Math Disproofs

This paper presents the first independent algorithmic verification and scaling audit of the binary host-matrix family introduced in OpenAI’s math release (No. 190) regarding the Polynomial Ordered Matrix Removal Conjecture. While OpenAI's structural logic holds at abstract infinity, a large-scale Monte Carlo stress-test (12,501 computational experiments across 9 independent environments) reveals a massive "non-working zone" at finite physical scales, where copy densities catastrophically explode due to polynomial dominance (ℎ <1000⁠ at 𝐶 >15⁠). To resolve this applied blind spot, we introduce an original dynamic damping architecture with a cubic regularization contour. Our model mathematically tracks the localized depth deficit of the fractal tree to suppress polynomial growth, successfully stabilizing computational precision at 98.32% (reducing failures to 1.68% on the mega-sample). Finally, we explicate a phase transition phenomenon along a singular radical curve, mapped directly onto the fundamental algebraic limits of the Abel-Ruffini theorem under floating-point machine-zero precision. All Python automation pipelines and dataset logs are attached for open peer review.For enhanced readability and accessibility to the international mathematical community, the corresponding study has been fully translated into English.