Artin Conductors and Parabolic Defect Across Collision Strata of Weighted Paired-Root Genus-Two Pencils

We study the parabolic cohomology of the rank-five primitive exterior-square local system associated with a weighted paired-root genus-two pencil. A classification of finite branch-point collisions, together with local monodromy calculations, yields an Artin-conductor formula for the geometric parabolic defect. We investigate the variation of global monodromy across generic weight strata and exceptional collision walls. In particular, we analyze a nonsymmetric nodal wall with full symplectic monodromy and a hidden-Möbius symmetry wall whose connected monodromy is a proper subgroup of \(\mathrm{Sp}_4\). In the latter case, quadratic descent and the action of the component group explain the disappearance of global primitive invariants. The resulting rank-five local system decomposes into a quadratic Kummer line and a rank-four tensor-induction component. The manuscript includes exact computational certificates and uses established results on semistable reduction, Hodge groups, geometric monodromy, and specialization. It is an independent research preprint that has not undergone journal peer review. A complete classification of all exceptional collision walls is not claimed.