{"id":"palomar/PALOMAR-2026-10-18-000030","url":"https://github.com/JD-Jones-ASES/persistent-sos/tree/54dc5a01cc16e850e3350ba0aa1bd8a8e5b67c5d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-18-000030-v1.json","repo":"https://github.com/JD-Jones-ASES/persistent-sos","tags":["math.OC","math.AG","msc:90C22","msc:14P10","msc:90C26","sum-of-squares","polynomial-optimization","semidefinite"],"score":0,"title":"Persistent failure of Euclidean quartic SOS exactness","trust":"high","domain":"math.OC","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"math.OC","summary":"An explicit rational homogeneous cubic with 25 monomials in 14 real variables has maximum one on the Euclidean unit sphere and admits a positive degree-four moment functional with value 500753357629/500000000000. For every positive real regularization parameter, quadratic strength and cubic strength, the associated quartic has an explicitly attained global minimum whose shift is not a sum of squares of real polynomials. A quantitative strict separation bounds every SOS lower bound. The polynomial is stationary at zero with negative definite Hessian. A second explicit 25-term cubic, certified…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-18","reactions":{},"formalized":true}