An eighth-degree polynomial with cyclic difference terms is nonnegative

$g=3\, \left( y-z \right) ^{2}{x}^{6}+9\, \left( y+z \right) \left( y-z \right) ^{2}{x}^{5}+ \left( 12\,{z}^{4}-9\,y{z}^{3}-2\,{y}^{2}{z}^{2}+12\,{y}^{4}-9\,{y}^{3}z \right) {x}^{4}+ \left( y+z \right) \left( 3\,{z}^{2}-4\,yz+3\,{y}^{2} \right) \left( 3\,{z}^{2}-2\,yz+3\,{y}^{2} \right) {x}^{3}+ \left( -9\,z{y}^{5}+3\,{y}^{6}-2\,{y}^{2}{z}^{4}-2\,{y}^{4}{z}^{2}+3\,{z}^{6}-9\,y{z}^{5}+8\,{y}^{3}{z}^{3} \right) {x}^{2}-3\,yz \left( y+z \right) \left( 2\,{z}^{4}+y{z}^{3}+2\,{y}^{2}{z}^{2}+{y}^{3}z+2\,{y}^{4} \right) x+3\,{y}^{2}{z}^{2} \left( {y}^{2}+yz+{z}^{2} \right) \left( y+z \right) ^{2}\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_31230 (Apache-2.0). Complete source proposition preserved; proof developed independently.