Remark: What this limit does and does not select

The quotient is generally large, and the state $\lambda$ need not be unique. It supplies a rigorous product-preserving observable interface, not a preferred vacuum, a renormalization-group limit, or a unique physical continuum theory. Scaling algebras in AQFT provide a more specialized framework with additional spacetime and continuity structure BuchholzVerch. We do not identify (eq:sequencequotient) with that construction.