Sharp Newton-edge bounds and cancellation families with one nonzero quadratic norm

Let g=(P,Q,R)=sum_{i=0}^{5} c_i x^{A_i} have six occupied vector coefficients, exactly one of which has nonzero norm for q(P,Q,R)=PQ+R^2. Over every field of characteristic different from two with a real-valued nonarchimedean valuation, we prove that q(g) has at most eleven strict lower Newton edges and at most ten edges of width one. Both maxima are attained simultaneously over every such nontrivially valued field. At every prime, integer examples have coordinate sparsity fourteen and exactly ten simple nonzero local roots of distinct valuations. The dyadic example has 228-bit input coefficients. The upper bound is computer assisted: a generic null-cone perturbation and a rank-three initial-matrix argument reduce the problem to 2,359 marked support patterns. Exact disjunction trees and integer linear identities exclude every pattern, without an exponent or precision cutoff. Six patterns require convexity inequalities forced by equal barycenters of exponent sums. The supplied verifier uses only the Python standard library. We also prove the sharp five-support bound of eight edges and construct, at every prime and every support size n>=8, one-norm examples with 2n+1 edges, of which 2n have width one. The envelope lemmas and the family construction are proved in full.