Definition: On-shell admission interface

A prospective admission consists of:

1. a unital quantum algebra $\mathcal{E}$ over $\mathbb{C}[[\hslash ,\kappa ]]$ and an injective homomorphism $j:{\mathcal{A}}_0[[\kappa ]]\to \mathcal{E}$;

2. a classical-symbol interpretation of the admitted elements on ${\mathcal{C}}_{\mathrm{sol}}$, compatible with the old finite-generator symbols;

3. lifts $Q({\mathcal{B}}_f)$ and $Q(\mathcal{T})$ with leading symbols $[{\mathcal{B}}_f]$ and $[\mathcal{T}]$ in ${{\mathcal{P}}_{\mathrm{mc}}}^{\mathrm{sol}}$;

4. agreement with the old inclusion whenever the symbol is represented by an old finite product;

5. an explicitly stated topology and continuity requirement if admission is to be obtained by kernel limits.

This definition names required data; it does not assert their existence.