Definition: Four same-model obligations

A same-model endpoint package for the declared code must supply:

1. Complete preparation. A justified code and a complete pure prepared isometry $P_0:C\to H_{\mathrm{tot}}$. Mixed ancillary preparations are purified and their purifiers remain in the complete system.

2. Complete evolution. A specified logical-input-independent unitary family $U_t$ on the complete system, on a justified time domain. Any energy-conservation claim has the separate hypotheses of Definition def:energy.

3. Justified access and endpoint comparison. Complete output identifications $F_t:H_{\mathrm{tot}}\to R_t\otimes B_t$ and factorwise isometries

   $$a_t:R_t\to R_{\ast },b_t:B_t\to B_{\ast }$$

   into common finite comparison spaces, preserving the declared access roles. Define

   $${\hat{V}}_t=(a_t\otimes b_t)F_t{U}_t{P}_0.$$

   There must be an endpoint isometry $V_{\ast }:C\to R_{\ast }\otimes B_{\ast }$ and a proved allowance

   $${\nu }_t=\min \{1,{\Vert {\hat{V}}_t-V_{\ast }\Vert }_{\infty }\}⟶0.$$

   The comparison maps are not allowed to move inaccessible logical registers into $R_{\ast }$.

4. Complete complement allowance. For ${\mathcal{E}}_{\ast }={\mathrm{Tr}}_{R_{\ast }}{\mathrm{Ad}}_{V_{\ast }}$, a state ${\sigma }_{\ast }\in \mathsf{D}(B_{\ast })$ and a proved bound

   $$d_{\diamond }({\mathcal{E}}_{\ast },{\mathcal{T}}_{{\sigma }_{\ast }})\le \zeta .$$

For a physical use of the package, all identifications and estimates must be justified within one microscopic model, on compatible domains and in a common regime of validity.