P(x,y) = F^4 + \sum_{k=1}^{3} A_k F^k + R(x,y) Q(x,y) = F^5 ...

Prompt

P(x,y) = F^4 + \sum_{k=1}^{3} A_k F^k + R(x,y) Q(x,y) = F^5 + \sum_{k=1}^{4} B_k F^k + S(x,y) where F(x,y) = x^{16} + y^{16}, and the successive deformation polynomials A_k, B_k, R, S are structured uniquely such that the Poisson bracket algebraically telescopically sums to 1 while violating cyclic extension requirements, establishing non-proper boundary loci S_f \neq \emptyset.