Definition: Environmental-memory exclusion obligation

A stronger witness must supply:

1. an exact null ${\mathfrak{N}}_{d,L,\mathcal{U}}$, or a justified union over allowed $L$;

2. a complete multitime record score $W$;

3. a proved upper bound

   $$b_{\mathrm{env}}\ge \underset{P\in {\mathfrak{N}}_{d,L,\mathcal{U}}}{\sup }{\mathbb{E}}_{P}W;$$

4. an admitted quantum-environment construction with

   $$\mathbb{E}W>b_{\mathrm{env}};$$

5. implementation and statistical allowances preserving that strict inequality.