The Tropical Geometry of Ore Systems: Modeling Mineralization as an Algebraic Amoeba over the Max-Plus Semiring

Abstract: Traditional geostatistics relies on the algebraic field of real numbers (ℝ,+,×), which fails to capture the threshold-dependent nature of distinct mineralization boundaries. This paper introduces a paradigm shift by modeling the "Mineralized Crustal Continuum" over the Tropical Semiring (𝕋,⊕,⊙). Drawing on the foundational work of Maclagan and Sturmfels (۲۰۱۵) and Mikhalkin (۲۰۰۶), we postulate that an ore body is not a Euclidean volume but the non-Archimedean Amoeba of an algebraic variety. We derive the Abhary-Tropical Conjecture, demonstrating that high-grade vein networks correspond to the Tropical Skeleton of the system’s defining polynomials. By utilizing Max-Plus algebra (Akian et al., ۲۰۰۶), we prove that the optimal cut-off grade is a solution to a tropical eigenvalue problem, providing a deterministic upper bound on reserve estimation through the geometry of Newton Polytopes.

کلیدواژه ها:

Tropical Geometry ، Max-Plus Algebra ، Algebraic Amoebas ، Newton Polytopes ، Predictive Metallogeny