Object ledger

Full-space nonrepresentability and finite-plane representability are compatible. The former requires equality on a space containing residual pure gauges. The latter asks for two interpolation conditions on a plane with no nonzero Schwartz pure gauge. Its annihilator is correspondingly much larger.

Likewise, field degree depends on what is quantized. With an external metric, a scalar-quadratic vertex has a linear first retarded scalar coefficient. With one metric oscillator, the coefficient has one oscillator factor and one scalar factor. Substituting a scalar stress into a Newton–wave inverse before forming the classical response is another operation, with a different degree and singularity structure.