Minimal certificate packet for an interacting recovery claim

A completed microscopic recovery result should archive:

1. The exact $N,\mathbf{J},\beta ,s,s^{\prime }$, source normalization, coupling polynomial, couplings, cutoffs, and packet functions.

2. The mode and occupation basis dictionaries, including source and carrier fermionic ordering.

3. The insertion isometry and the complete residual inventory.

4. The finite Hermitian Hamiltonian and the exact definition of its propagator. A floating-point array is not the exact specification unless a proved error enclosure accompanies it.

5. All accessible and complementary logical matrix-unit outputs.

6. A rigorously feasible replacement state or complete decoder, together with certified positivity and trace-preservation conditions.

7. Validated trace-norm upper bounds and any arithmetic allowances.

8. The regulator parameters selected from Corollary cor:regulator-selection, or sharper proved bounds.

9. A declared time or a uniform time interval, with a proved continuity allowance when finite sampling in time is used.

10. For a gravitational claim, the separately derived state, observable, energy, geometry, and radiation-access comparisons on the same interval.

11. For an endpoint claim, the asymptotic identification, bound-sector audit, complete residual channel, order of limits, and separate gravitational endpoint.

The finite-channel interface in the supplied Em03-H is a useful documentary comparison for items involving complete purifications and matrix units CheungEm03H. Its eigenvector-selected code and finite path are not substituted for the physical loading and continuum evolution specified here.