Proposition: The initial inaccessible diary

At cut zero in the declared model, for every $U$,

The initial complement is reversible when completely accessible.

Proof. A unitary on the vault does not change the early marginal:

The recovery benchmark follows from Lemma lem:KSW. The complement is

Undoing $U$ and tracing $HF$ left-inverts it.

For any replacement state, this left inverse maps its comparison to an identity-versus-replacement comparison, whose distance is at least $a_d$. Conversely, comparing with ${{\mathcal{C}}_0}^U(I_L/d)$ and using contraction gives distance at most $d_{\diamond }({\mathrm{id}}_L,{\mathcal{T}}_{I_L/d})=a_d$.