Scope and the four levels.

and the four levels.{ The preparation width $0<\epsilon <T$, preparation data $f,g$, and smooth time-only ramp ${\sigma }_{\epsilon }$ are fixed. The interaction switch ${\chi }_{\mathrm{I}}\in {C_c}^{\infty }({\mathbb{R}}^4;\mathbb{R})$ is independent of these data.

The four levels are:

A nonzero coefficient at one level does not establish nonvanishing at a later level.

The construction is conditional on the explicitly stated root hypotheses. No sharp-width limit, global adiabatic limit, ultraviolet completion, all-orders time ordering, or interacting gauge identity is claimed. }