Boundary-Response Reconstruction in Canonical ACRF-4: Certified Local Recovery of the Nine-Dimensional Consequence Quotient from Relational Boundary Histories and Controlled Boundary Probes

This note establishes a model-specific boundary-response reconstruction result in canonical finite ACRF-4. A prior Registration Theory holography audit showed that the instantaneous three-coordinate relational boundary B_SC=(A,B,C) is not generically sufficient to determine the full nine-dimensional consequence-minimal host-boundary quotient. The present note tests a different proposition: whether the complete consequence-bearing state can be reconstructed from relational boundary history or from controlled boundary interventions and subsequent boundary-only responses. Using the previously published canonical ACRF-4 dynamics and certified generic witness, the passive three-step boundary-history map R_3(q)=(B(Fq), B(F^2q), B(F^3q)) has a 9x9 Jacobian of rank nine. Its high-precision determinant is approximately 1.3833843350670083e-10. Interval automatic differentiation on the radius-1e-12 witness box gives the enclosure [1.3833629032709224e-10, 1.3834057672127077e-10], excluding zero throughout the box. By the inverse function theorem, the complete nine-dimensional quotient is locally reconstructible from three successive future relational-boundary readouts. A second, independent test uses three controlled boundary perturbations of amplitude 0.2 in the A, B, and C directions. For each probe, only the change in the next two relational-boundary readouts is retained. The resulting 18x9 controlled-response Jacobian has rank nine. A fixed 9x9 response minor has high-precision determinant approximately 1.5123876691907708e-19, with interval enclosure [1.5123523692839217e-19, 1.5124229697956800e-19], again excluding zero throughout the declared witness box. Thus boundary-only response data locally reconstruct the entire consequence-minimal quotient even though the instantaneous boundary state does not. A deterministic robustness audit sampled 300 regular states at each coordinate radius 0.01, 0.05, and 0.10 around the witness; both reconstruction maps had numerical rank nine in all 900 samples. Analyticity then gives generic local full rank away from an analytic exceptional set on the corresponding connected regular component. The result provides a concrete finite-dimensional Registration Theory realization of consequence reconstruction rather than literal boundary storage. It is structurally motivated by inverse-boundary reconstruction, including OpenAI's October 5, 2026 preprint "Determination of a metric and a unitary connection from one boundary patch," but it does not import primitive metric, manifold, gauge, or elliptic structure into Registration Theory. It does not establish global injectivity, an area law, the Bekenstein-Hawking coefficient, gravitational holography, or universal boundary-response exactness in Registration Theory. The upload package includes the PDF timestamp note, LaTeX source, a reproducibility script, and the complete certificate output.