Tuza's Conjecture for Split Graphs with an Eight-Vertex Clique Part and Two Neighborhood Types

For a graph G, let \( \nu_{\triangle}(G) \) be the largest number of pairwise edge-disjoint triangles and let \( \tau_{\triangle}(G) \) be the smallest number of edges meeting every triangle. Tuza's conjectured that \( \tau_{\triangle}(G)\leq 2\nu_{\triangle}(G) \) for every graph. We prove the conjecture for every split graph with a specified split partition \( V(G)=C\mathbin{\dot\cup}I \) such that \( |C|=8 \), for which the triangle-active vertices of I have at most two distinct neighborhoods in C. The result allows arbitrary multiplicities of the two types. The infinite statement is reduced to 44,702 canonical cases by an exact multiplicity-truncation lemma and symmetry. Each case carries an explicit triangle cover and an explicit edge-disjoint triangle packing, checked by an independent standard-library verifier. We also give exact cover and packing reductions for arbitrary split graphs and a maximum-cut criterion that settles, at \( |C|=8 \), every instance whose independent-side neighborhood 2-shadow has at most seven edges. The unrestricted split-graph and interval-graph cases remain open.