Can a huge polynomial be represented by a small matrix? This research candidate studies a geometric object called the essential variety, which arises in the mathematics of two camera views. A generic section meets it in ten points. The associated degeneracy polynomial detects where that intersection degenerates. Although the form has degree thirty in its geometric coordinates, the manuscript gives a compact recipe using a ten-by-ten trace matrix. A correcting determinant, raised to the fourth power, removes the apparent denominator. The difficult part is proving that this cancellation works globally, including beyond the convenient coordinate chart. The written argument follows the one intersection point that escapes to infinity and measures the resulting pole. It then identifies the global polynomial by its degree and vanishing. The same construction applies to symmetric four-by-four matrices of rank at most two. The package includes exact rational code, a boundary evaluator and controls for tangencies and misleading projections. A published symmetric example gives zero at parameter one hundred and ninety-four and a nonzero value at one hundred and ninety-five. Those finite checks test the implementation. The written proof supports the general mathematical result. Classical trace formulas and earlier specialized computations are credited. Historical priority remains uncertain, and no numerical stability or camera-estimation speedup has been demonstrated. This is an Evidence Press unrefereed candidate released on 7 September 2026. The full paper and evidence are linked. The voice is AI-generated. This audio is a communication aid, not additional mathematical evidence.