Definition: Physical acquisition and identification package

A package for this target consists of:

1. A named physical source model on a specified finite input space ${\mathcal{H}}_{\mathrm{P}}$, with fixed injection templates ${\sigma }_b,{\sigma }_d$ and an effect ${F_b}^{\mathrm{P}}$ satisfying

   $$\mathrm{Tr}({F_b}^{\mathrm{P}}{\sigma }_b)=1,\mathrm{Tr}({F_b}^{\mathrm{P}}{\sigma }_d)=0.$$

   Its promised source family is

   $${\sigma }_{\theta }=\theta {\sigma }_b+(1-\theta ){\sigma }_d.$$

   Therefore the named source observable obeys $\mathrm{Tr}({F_b}^{\mathrm{P}}{\sigma }_{\theta })=\theta$. This excludes source-dependent selection from being silently identified with injection weight.

2. A $\theta$-independent CPTP source comparison map $\mathcal{E}:\mathcal{L}({\mathcal{H}}_{\mathrm{P}})\to \mathcal{L}({\mathcal{H}}_J)$ and a proved allowance

   $$d_{\mathrm{tr}}(\mathcal{E}({\sigma }_{\theta }),{\tau }_{\theta })\le e_{\mathrm{src}}\text{uniformly in }\theta .$$

   It is sufficient to prove this allowance on the two source templates, with the corresponding targets $0,1$.

3. A named microscopic physical evolution, its auxiliary preparations, transport stages, nuisance domain, and complete detector instrument, yielding a CPTP record channel

   $${\mathcal{B}}_{\eta }:\mathcal{L}({\mathcal{H}}_{\mathrm{P}})⟶\mathcal{L}({\mathcal{H}}_C).$$

   All attempted outcomes and all physical loss, failure, or rejection branches are retained. Its measured-name access rule is specified separately from its matrix representation.

4. A derived or independently certified complete comparison

   $$d_{\diamond }({\mathcal{B}}_{\eta },{\mathcal{A}}_{\eta }\mathcal{E})\le e_{\mathrm{acq}},$$

   uniformly over the admitted nuisance and input interface. The map $\mathcal{E}$ in this comparison need not be a physically executed preprocessing, but its domain and meaning must be explicit.

5. A calibration event and independent attempted-run contract of the form in Assumption ass:statistics. The correspondence between physical field/turbulence parameters and $\eta$ is part of the package. It is not inferred from the notation $\hat{n}$.

6. If competing physical source interpretations are to be excluded, their complete promised record families and allowances are supplied, together with the scope of the candidate list.