Interpretation and externally supplied corrections

A departure from ${\rho }_0$ can arise from altered preparation, ordinary matter interactions, changed scattering, or a changed background. It does not by itself identify quantum gravity or information recovery.

If a separate theory supplies

then the certified lower bound is obtained by subtracting $r(\lambda )$, both apparatus errors, and any proved cutoff comparison from $|\lambda p_1(E)|$. This is a substitution rule, not an evaluated effective-field-theory correction. No effective action, loop coefficient, regulator removal, or microscopic horizon model is introduced by that formula.

Figure fig:discrimination is the operational gap. A specified ideal effect gives a probability difference. Both implementation errors and, when trials are used, the finite-sample allowance are subtracted. A positive lower bound certifies a record departure. It does not name the physical cause.