arXiv:2610.22741v1 Announce Type: new Abstract: Additive manufacturing, also known as 3D printing, is significant for its use in industries such as aerospace, robotics, medicine, and construction. However, digital mesh files remain vulnerable to geometry defects which can be introduced through malicious tampering or designer error. This can lead to hampered structural integrity and impede its use due to unexpected degradation of the part. To address these challenges, we propose SAMS, a multi-layered hierarchical graph framework designed to analyze meshes to enhance the Security of Additive Manufacturing Systems. SAMS captures geometric and topological information across mesh, facet, and surface levels, providing an adaptable architecture for targeted mesh processing tasks. We evaluate SAMS's accuracy against existing mesh processing tools. The graph construction results in rich structural representation and has the potential to significantly reduce downstream analytical complexity when detecting vulnerabilities. This paper presents SAMS, its formal graph-theoretic properties, and releases an open-source Python 3.12 implementation on GitHub (https://anonymous.4open.science/r/SAMS-graph-classes/) to facilitate future research in secure additive manufacturing systems software.