A long-standing part of the Polydegree Conjecture asks whether one family of plane polynomial automorphisms lies in the closure of another for every degree. This anonymous, unrefereed candidate proves the full case indexed by e equals three. The first step replaces an auxiliary determinant with a geometric question: can we find one smooth common zero of two coefficient polynomials where a third does not vanish? An explicit Fourier limit provides model zeros for the two difficult residue classes. Quantitative Newton--Kantorovich bounds then carry those zeros to all sufficiently large degrees. Exact finite-field certificates cover degrees two through one hundred, one residue class has an exact special point, and ninety-seven thousand and thirty-three outward-rounded Arb calculations close the remaining finite interval with no failures. A separate exact-rational envelope covers every later degree. The public package includes the formulas, exact locators, every case row, receipts, code, manifests and review responses. This is a producer-side theoretical and computer-assisted proof. It has not been independently implemented or reconstructed, formally verified, reviewed by an external specialist, or peer reviewed. The fixed-e extension remains a conjectural research programme. This synthetic-voice briefing is a communication aid, not additional mathematical evidence.