An earlier actual label is protected separately

9 An earlier actual label is protected separately

For the full initial offset support,

The compact comparison is therefore still in the common potential before $t_a$ and has completed writing at $t_b$. These guards concern a comparison support; they are not a claim that the exact clock has compact support at later times.

Before $t_a$, use

Its residual norm is at most $t\norm{\varphi''''}/(4M^2)$. Both the exact common auxiliary evolution and each exact driven sector differ from $F_1$ by at most $t_a^2\norm{\varphi''''}/(8M^2)$. Therefore

This expansion has not discarded any exact clock tails.

Let $\rho_r,j_r$ be the isolated spinor rotor current. Its initial density is $1/2$, and circle Sobolev/energy estimates give

Exact sector factorization bounds the pretrigger wave and its $X$ derivative errors by $\epsilon_{\rm pre}$ and $(K/h)\epsilon_{\rm pre}$. Thus

The isolated lifted cumulative rank along the coupled ordinary path obeys

including its circulation. Hence

This is the physical clock-to-label error used in the periodic-current section. A global wave norm alone is not used as its replacement.