The N=8N=8 supergravity Hamiltonian as a quadratic form

We conjecture that the light-cone Hamiltonian of N=8N=8 supergravity can be expressed as a quadratic form. We explain why this rewriting is unique   to maximally supersymmetric theories. The N=8N=8 quartic interaction vertex is constructed and used to verify that this conjecture holds to order κ2κ2.