Hawking-mode calibration and compatibility limits

Consequently arbitrary exact local thermal restrictions cannot be promised independently at every step. A target $a_j=a_d(q_j)$ must satisfy (eq:sumcompatibility), and the parameters $q_j$ must first be obtained from an actual declared source calculation if an astrophysical calibration is intended.

The key block is deliberately not Hawking-like in a small-tail regime. For $g=d^2$, its state is ${I_g}^{(1)}/g$, and

The minimum follows by maximizing the one-particle probability at $q=1/(g+1)$. Thus this construction does not claim uniformly small thermal deviations for all emitted blocks.

and symmetry scope. The logical operations act inside a degenerate fixed-charge code. No claim is made about preserving coherent superpositions of arbitrary different charge sectors with the same rules. Conservation can impose additional recovery constraints in scrambling models and symmetry-covariant codes NakataWakakuwaKoashi2023,FaistEtAl2020. Those constraints are not removed by assuming sufficient degeneracy without disclosing it.