Nonperturbative meaning

No proof above expands in a gravitational coupling or assumes that $a,k,b$ are small. Large allowances remain legitimate but can make the certificate vacuous. Thus “beyond a small-correction input” means that the inequalities remain valid for the declared channels; it does not mean that an unprovided quantum-gravitational channel has been constructed.

If a physical bounded observable is represented on the code by $O$, and a separately proved dictionary allowance satisfies

for the named preparation class, the complete expectation allowance is

where $a_{\mathrm{readout}}$ is a distinct detector allowance. The dictionary and detector estimates are inputs to this statement. Unbounded observables require an additional domain and energy-constrained analysis absent from this finite contract.