The preceding paper of this series established a bounded wild continuation theorem for coordinate-free renormalized tail orbits. On admissible ramified covers it recovered the full irregular formal type, the logarithmic residue package, and the finite geometric Stokes skeleton of the associated quantum packet. What it still left hidden is the analytic content of the divergent regular factors themselves. In the genuinely irregular regime those factors are seldom convergent; they are only sectorially meaningful after Borel--Laplace summation, and their jumps across singular Borel directions are encoded by alien calculus rather than by geometric Stokes matrices alone. The present paper treats exactly that next layer, again in a sharply delimited but substantial setting. We remain within bounded ADE miniversal families and coordinate-free smooth simple-pole branch models. We assume that on each admissible irregular chart the active wild blocks have bounded Poincar\'e rank, finite action sets in the Borel plane, simple algebraic-logarithmic Borel singularities, and one-summable formal regular parts in every non-singular Laplace direction. In this bounded resurgent-wild regime, the renormalized tail orbit determines not only the irregular packet of the previous paper but also its hidden resurgent structure. The first main theorem is a local Borel--Laplace closure theorem. It proves that after removal of the explicit exponential and logarithmic singular factors, the sectorial packet is the Laplace sum of a unique common simple-resurgent formal series. The orbit functorially recovers the finite action packets, their singular exponents, and the principal singular coefficients of the Borel transform. Thus the full regularized wild packet canonically lifts to a resurgent packet. The second main theorem is an alien bridge theorem. For every observed Borel singularity the orbit determines a constant bridge operator B_ and a scalar alien tau-coefficient c_ such that \ _ J = J B_, _ = c_. \ The lateral Borel sums are glued by ordered exponentials of these bridge operators, so the orbit recovers not only the geometric Stokes skeleton in the base variables but also the full first-level alien transport in the summation variable. The third main theorem is a resurgent quantum Torelli statement. On a fixed admissible compact resurgent cover, one normalized median-summed regular sector together with the orbit-recovered formal type, action local system, and alien bridge data determines the entire resurgent quantum packet up to filtered primitive scalar gauge and blockwise symplectic conjugacy. Equivalently, the orbit determines the Borel--Laplace continuation of the irregular TEP structure in the stated bounded regime. The fourth main theorem gives a quantitative finite-Borel detector. From finitely many sectorial orbit probes, finitely many lateral direction pairs, and finitely many discrete Borel samples over a bounded observation window, one asymptotically recovers the leading action packets, singular exponents, principal bridge coefficients, truncated Stokes automorphisms, and median packet values, with error \ (N^-1+N+N+N+N+N). \ The statement is intentionally local and finite-horizon. It is not presented as a globally conditioned numerical algorithm under arbitrary noise or in the presence of dense unresolved Borel webs. Conceptually, the paper identifies the next rigidity threshold beyond wild Stokes data. In the bounded resurgent-wild regime, the renormalized tail orbit determines not only formal exponential type and sectorial Stokes jumps, but also the resurgent Borel singular support and its alien bridge calculus.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.