Verification, scope and references

6. Verification and scope

The paper reports replaying its nine verification suites from a fresh extraction. All 149 results matched the reference outputs: 122 exact symbolic checks, 26 reproduced failure controls, and one numerical diagnostic. The checks cover the Killing normalization, both routes to the charge identity, boundary coefficients, scalar inversion identities, and explicit on-shell and off-shell examples. The compactly supported lapse and the dimension-dependent anchoring estimate are analytic additions. The fixed-radius example follows from the exact Bessel formula; its numerical diagnostic illustrates the zero and recovery at another radius.

The equivalence is first order and concerns the Einstein residual in the stated class. The readout depends on the aperture and the shared holographic inputs. Restricting to a time slice leaves an infinite-dimensional metric kernel that includes genuine off-shell examples. Additional slices and boosts change the available contractions. Once those contractions span, the radial equations still require boundary information. Scalar inversion, polarization and Ward data therefore play distinct roles in recovering the local equations.

Funding

This work received no external funding.

Verification materials

The verification package for this edition includes targeted checks of the corrected transverse profile and instructions for replaying the original suites. Scripts and reference outputs are also available from the Zenodo record.

References

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