Conditional Observable Completeness in Near-Extremal Black-Hole Inference

A finite set of exterior observables may determine the parameters of a specified near-extremal black-hole response model, yet this does not establish model-independent completeness. We formalize the distinction. For a chosen forward model, parameter domain, labeled channels, covariance, and nuisance family, local completeness is a rank property of a dimensionless or whitened response Jacobian, whereas global completeness requires injectivity over the declared domain. Both are conditional. Using θ = (E_i,C,Ω_H,Φ_H), with C = E_b⁻¹ as in Paper B and E_b the breakdown energy used in Paper A, we derive the channel-diversity condition m₁q₂ - m₂q₁ ≠ 0 needed to separate rotation from electric potential, and explain why finite-frequency information is needed to break zero-frequency energy-scale degeneracies. We then show why local full rank does not imply global uniqueness or finite-precision reliability, why calibration freedom can make a formally full-rank inverse practically unusable, and why agreement with a finite-dimensional throat model cannot exclude enlarged models or additional quantum-gravity degrees of freedom. The paper deliberately introduces no unverified channel counts or numerical completeness claims. Its result is an auditable framework for conditional observable completeness and a clear boundary between Paper B reconstruction and stronger completeness claims.