HDBLAST: Scalar Junction Consistency and a Corrected Static de Sitter Branch

We examine scalar junction consistency in a specified five-dimensional Einstein-scalar shell model. The constant bulk field phi=1 solves the bulk scalar equation but fails the scalar boundary condition for the registered nonzero detuning. We construct nearby nonconstant scalar-profile candidates from a regular cone and impose both gravitational and scalar junction conditions. At delta=0.001 and c=0.5975949350280132, the candidate has phi_b=0.9999159473169134 and H_b squared=5.9240147943293e-5 in model units. Six detunings, two producer tolerances, and 18 separate second-order Einstein integrations support numerical consistency. A regular Gegenbauer solution yields the leading scalar shift and the second-order expansion-rate correction. The registered expansion-rate correction is approximately -7.87 parts per million relative to the metric-only comparison. The deposit includes a self-contained research manuscript and a computational supplement with source code, numerical profiles, exact identities, independent checks and reproduction instructions. It concerns reproducible floating-point static candidates and analytical consistency results. Stability, dynamical attraction, a global connection to the original configuration, interval-certified existence and a hot Big Bang mechanism are not established. No claim of external mathematical novelty is made. This is a separate companion study referencing the earlier conditional linear-response record (10.5281/zenodo.22347452). It does not revise or extend that record's certificate to this nonlinear static problem. AI tools assisted with derivations, software, numerical checking and manuscript preparation; internal computational reviews are not external peer review.