Non-Semisimple Quantum Continuation from Coordinate-Free Renormalized Tail Orbits:\ Logarithmic TEP Closure, Nilpotent Wall-Crossing, and Finite-Chamber Recovery

The preceding paper of this series solved the global semisimple problem for coordinate-free renormalized tail orbits on the semisimple complement of a bounded ADE discriminant. It glued the local Givental--Teleman packets on the ordered universal cover and recovered the global semisimple quantum monodromy. What it did not do was to cross the discriminant itself. The present paper crosses that boundary in a sharply delimited regime: coordinate-free smooth simple-pole branch families attached to a bounded ADE miniversal family, after passing to a finite ordered cover on which the relevant discriminant stratum becomes normal crossing and each irreducible component carries a single collision block. Within that regime we prove that the renormalized tail orbit determines the logarithmic quantum continuation across the wall. First, the semisimple packet extends uniquely to a local logarithmic TEP packet on every admissible collision chart. The extension is encoded by orbit-recovered nilpotent residues N₁, , Nᵣ and rational tau exponents ₁, , ᵣ; equivalently, after a collision-adapted holomorphic normalization, the full singular part is forced into the explicit factors \ J=J^=₁ʳ t_^N_/ (2 i), =^=₁ʳ t_^_. \ Second, adjacent semisimple chambers are glued by rigid wall data (Pₑ, Kₑ, Nₑ, ₑ, ₑ), where Pₑ is the permutation induced by relabeling the colliding canonical idempotents, Kₑ is a constant filtered symplectic upper-triangular loop, Nₑ is the nilpotent wall residue, ₑ is the local tau exponent, and ₑ is the regularized tau-line multiplier. These objects define a logarithmic quantum monodromy groupoid extending the semisimple quantum monodromy of the previous paper. Third, one normalized generic semisimple fiber together with the wall data determines the entire non-semisimple logarithmic quantum packet on the chosen normal-crossing compactification, up to filtered primitive scalar gauge and filtered symplectic conjugacy. Fourth, on a fixed compact region with a finite admissible chamber cover, finitely many scalar orbit probes over a bounded observation window asymptotically recover the collision partition of each observed wall, the nilpotent rank profile Nₑʲ, the truncated filtered symplectic factors Kₑ, and the tau exponents and multipliers, with error (N^-1+N+N). The detector theorem is stated explicitly as a local finite-horizon asymptotic result; it is not claimed to be a globally conditioned arbitrary-noise algorithm. A conceptual dichotomy appears. Some walls are semisimply innocent after regularization: their only new effect is a scalar tau exponent. Genuine non-semisimple behavior begins precisely when some Nₑ0. Then the orbit detects logarithmic residue data invisible from the open semisimple packet alone.