X72-56: Rigorous Adjoint-Tail Bound and Central-Coefficient Positivity

Building on Round 55's compression of the entire obstruction into a single positivity question, this round no longer relies on finite-truncation extrapolation, but instead builds a Banach fixed-point tail construction for the infinite-dimensional adjoint recursion, using exact algebraic root isolation to prove that the tail map becomes a strict contraction beyond a sufficiently deep sideband — thereby rigorously proving the unique existence of a regular, bounded, minimal adjoint mode. This rigorously establishes a positive lower bound on the central coefficient, and combined with Round 55's same-sign result, rigorously excludes a complete second-order analytic rescue on both source-hidden circles at the normalized viscosity — the first time in this branch that a rescue question has been closed by an infinite-tail argument, rather than by finite truncation or numerical extrapolation. Route halts at STOP-C60 (viscosity-parameter continuation / global-hidden-manifold gap): this closure holds only for a single normalized viscosity value, does not yet cover all positive viscosities, and does not cover hidden manifolds outside this circular-Beltrami reference frame, handed to the next round to perform the viscosity continuation; this round also includes a numerical-verification script.