A researcher presents an integer-native geometric framework that reduces lattice point enumeration complexity from O(r^N) to O(r^2) by decomposing high-dimensional spaces into orthogonal submanifolds and using discrete integer operations instead of continuous Euclidean methods. Four preprints establish theoretical foundations, asymptotic proofs, and C++ implementations verified against OEIS sequences, with hardware benchmarks demonstrating enumeration of billions of lattice points without floating-point arithmetic.
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