We present the Variational Curvature Governance (VCG/CAFVCG) protocol for black-hole ringdown audit together with a theoretical Gen-6 Variational Curvature-Transfer Governance (VCTG) extension based on curvature-first conditional-path covariant flow. In the implemented VCG model, black-hole ringdown is treated as a protocol-level observational probe of curvature-response structure rather than solely as linear perturbation on a prescribed Kerr background. Within this modeling language, the core mass-response observable is formulated axiomatically as the second-order scale-flow response of a governance scalar, m2=M0∂s2log⁡B,m_2 = M_0\partial_s^2\log B,m2=M0∂s2logB, while an optional hierarchical extension is written as m≥2=M0∑q=2n(τq∂s)qlog⁡B.m_{\ge2} = M_0 \sum_{q=2}^{n} (\tau_q\partial_s)^q \log B.m≥2=M0q=2∑n(τq∂s)qlogB. The currently implemented waveform protocol incorporates governance-dependent frequency and damping corrections together with a Structure-Error-Correction (SEC) operation. In the present numerical calculations, SEC is realized by a tanh-type soft-threshold engineering surrogate; it is not identified with the full covariant SEC projection introduced in the Gen-6 theory. Numerical audits reported in this study compare a GR baseline with VCG (Gen-4) and CAFVCG (Gen-5) templates on selected windows of publicly available LIGO strain data. Under the declared window and preprocessing settings, VCG reduces normalized mismatch by 2.7%2.7\%2.7%–44.5%44.5\%44.5% relative to the GR baseline, while Gen-5 CAFVCG achieves reductions of 3.0%3.0\%3.0%–48.2%48.2\%48.2%. SEC-processed residuals exhibit relatively clean periodic geometric structures consistent with the expected form of the second-order mass-response ansatz. These results are protocol-level model-comparison benchmarks; they do not establish that VCG replaces General Relativity, nor do they show that the present numerical implementation already realizes the full Gen-6 dynamics. The theoretical Gen-6 extension is formulated here as Variational Curvature-Transfer Governance (VCTG). VCTG retains the curvature-first ontology of VCG/CAFVCG, but replaces generic non-local curvature borrowing by a relative-curvature-deviation-ordered conditional-path architecture. In this formulation, GR contains only the passive classical metric governed by the Einstein equation, whereas VCG decomposes the metric structure into a passive metric and an active-governance metric component. SEC acts as a cross-variable correction mechanism among the passive metric, the active-governance metric, curvature deviation, the governance scalar, and the system state. Therefore, the GR-compatible retraction of VCG is not defined by the vanishing of the total metric evolution, but by the vanishing of the active-governance metric correction: (∂tgμν)gov=0,or equivalently∂tgμνactive=0.(\partial_t g_{\mu\nu})_{\rm gov}=0, \qquad \text{or equivalently} \qquad \partial_t g_{\mu\nu}^{\rm active}=0.(∂tgμν)gov=0,or equivalently∂tgμνactive=0. A directed VCTG channel (a←b) (a\leftarrow b) (a←b) is activated only when the receiving region (Da) (D_a) (Da) exhibits sufficiently higher relative curvature deviation than the supply region (Db) (D_b) (Db). If a more stable admissible region is detected along an active corridor, the supply mechanism may be conditionally re-anchored. Only activated relative-deviation-ordered paths enter the non-local chain variation, after which SEC acts as a covariant proximal projection onto the admissible governance manifold. Under coercive curvature-energy, smooth conditional gates, bounded CAF kernels, non-amplifying path coverage, positive effective mobility, SEC Lyapunov descent, absorbable geometric and routing remainders, spatial continuation control, and finite external input assumptions, Appendix F gives a conditional covariant non-singularity theorem that elevates the computational stability mechanism of Appendix E to the ideal Gen-6 governance spacetime. The present work therefore supplies a quantitative ringdown benchmark and a mathematically auditable covariant extension for future strong-field and nonlinear-structure tests, rather than an unconditional foundational proof.