The preceding paper of this series showed that in a bounded resurgent-wild regime the renormalized tail orbit determines the finite Borel singular support of the regularized packet together with its first alien bridge operators. That theorem still left a structural gap. Bridge coefficients themselves are not the final invariant: under gauge change they reorganize, and what persists is the full noncommutative transport law obtained by crossing singular Borel directions in all admissible orders. The natural next step is therefore a Riemann--Hilbert classification in which the orbit is matched not merely with singular coefficients, but with a canonical alien character object. This paper develops exactly that classification, again in a deliberately bounded but nontrivial setting. We remain within bounded ADE miniversal families and coordinate-free smooth simple-pole branch models. On every admissible irregular chart we assume finitely many active wild blocks, a finite action set in the Borel plane, simple algebraic-logarithmic singular jets, one-summability away from the induced singular rays, and blockwise separation sufficient to order the exponential scales observed by the renormalized tail orbit. These hypotheses are strong enough to make the alien transport finitely generated, and weak enough to preserve genuinely nonabelian Stokes interactions. The first main theorem is a local alien closure theorem. It proves that the regularized orbit determines, for every singular Borel direction, a canonical prounipotent alien Stokes factor obtained by ordered exponentiation of orbit-recovered bridge jets. Equivalently, the orbit determines a point in every finite-depth alien character variety associated with the action graph of the chart. The second main theorem is an exact resurgent Riemann--Hilbert classification theorem. It identifies bounded resurgent quantum packets, modulo filtered primitive scalar gauge, with bounded alien character data consisting of the formal irregular type, the geometric Stokes skeleton, and the full family of alien Stokes factors. Thus the orbit classifies the packet by a genuinely coordinate-free moduli object rather than by isolated bridge coefficients. The third main theorem is a global median descent and Torelli theorem. On an admissible compact resurgent cover, one median packet on one chamber together with the orbit-recovered character point determines the entire packet by ordered transport along the combined geometric--alien groupoid. In particular, the resurgent packet is reconstructed globally from one chamber and one character point. The fourth main theorem is a quantitative finite-contour detector. From finitely many regularized orbit probes, finitely many lateral direction pairs, and finitely many contour samples in the Borel plane, one asymptotically recovers the truncated alien character point up to depth M with error \ (N^-1+N+N+N+₍, ₌). \ The statement is intentionally local and finite-horizon; it is not presented as a globally conditioned arbitrary-noise numerical algorithm. Conceptually, the paper upgrades the resurgent layer from a collection of bridge equations to an exact character theory. In the bounded regime treated here, coordinate-free renormalized tail orbits determine not only the Borel singular support and the alien bridges, but the full alien transport class and its global median descent.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.