Analytic Continuation Across a Singular Constraint Surface in a Seven-Dimensional Nonlinear Dynamical System

A scalar analytic constraint on a seven-dimensional nonlinear state system leads, after differentiation, to a constraint-preserving feedback law whose denominator may vanish. We derive a local analytic continuation criterion at a singular point using a vector Briot–Bouquet reduction. Its hypotheses require an exact simultaneous zero of four constraint quantities, a nonzero directional derivative, and a nonresonance condition; the resulting germ is locally unique in the analytic class and preserves both constraints. For a fully specified rational-decimal model, we describe a computer-assisted existence certificate for a transverse crossing and a separate interval enclosure for the second Taylor coefficient of the auxiliary scalar. We distinguish the analytic theorem from its computational application and provide explicit sign checks and reproducibility requirements. The conclusions concern only local continuation of the mathematical model.