" The main theoretical paper and an appendix with manual numerical verifications of the four algorithmic pillars."

I'm Leonardo, the author of this paper. I've been researching a geometric algebra framework called NLS (Número Lo Shu).

The core problem I tackled: In computational algebra, solving coupled systems of multivariate polynomial equations (like intersections of complex 3D surfaces) usually requires expanding terms, leading to a combinatorial explosion (e.g., Gröbner bases). Standard matrix operators treat matrices as black boxes of numbers.

The NLS framework proposes a different approach: enforcing a strict geometric equilibrium (conservation and opposite-node symmetry) on a parametric 3x3 matrix. This forces the algebra to collapse into a highly predictable structure.

The paper outlines four mathematical pillars that provide a computational advantage:

1. Determinantal Factorization: The determinant of the multivariate matrix naturally collapses into a simple product of three terms (det = 9 * P * Mass). No expansion needed.
2. Orthogonal Decoupling: Vectorized NLS tensors decouple into three independent 1D scalar systems, reducing complexity from exponential to linear.
3. Closed-Form Spectrum: Eigenvalues are explicitly known without computation (O(1) spectral analysis).
4. Closure under Inversion: The inverse of an NLS matrix is structurally another NLS matrix, ensuring zero information loss in physics simulations.

I propose this could be useful for computational geometry, fluid dynamics (guaranteeing conservation axiomatically), and GPU shaders. I’d love to hear what the math and CS folks here think about this approach.