Cutoff grammar

The symbols have different meanings:

$\epsilon$, Model 1.

A smooth replacement of a sharp initial-time edge in a scalar smearing. It is removed at the unitary and record levels.

$R$, Model 2.

A simultaneous gravitational infrared and ultraviolet mask and a scalar ultraviolet mask. It is removed at fixed number cutoff $M$.

$M$, Models 2 and 3.

A particle-number projection on the Hilbert space of that model. It remains finite in every measured evolution considered here. Statements uniform for sufficiently large $M$ do not assert an instrument limit as $M\to \infty$.

$\Lambda$, Model 3.

A scalar momentum cutoff. It is retained in its measurement theorem. A classical or coherent expectation limit is used only to select one sufficiently large finite value.

$N$, Model 2.

A finite-rank projection on gravitational one-particle kernel legs. It is not a particle-number cutoff.