Algebraic Obstructions and the Collapse of Elementary Structure in the Kronecker Problem

While Kronecker coefficients g(λ,μ,ν) with bounded rows are polynomial-time computable via lattice-point methods, no explicit closed-form formulas have been obtained for genuinely three-row cases in the 87 years since Murnaghan's foundational work. This paper provides such formulas for the first time and identifies a universal structural boundary at parameter value 5 where elementary combinatorial patterns collapse. We analyze two independent families of genuinely three-row coefficients and establish that for k leq 4, the formulas exhibit elementary structure: oscillation bounds follow the triangular-Hogben pattern, and polynomial expressions factor completely over mathbb{Z}. At the critical threshold k=5, this structure collapses: the triangular pattern fails, and algebraic obstructions - irreducible quadratic factors with negative discriminant - emerge. We develop integer forcing, a proof technique exploiting the tension between continuous asymptotics and discrete integrality. As concrete results, we prove that g((n,n,1)³) = 2 - \(n mod 2\) for all n geq 3 - the first explicit formula for a genuinely three-row Kronecker coefficient - derive five explicit polynomial formulas for staircase-hook coefficients, and verify Saxl's conjecture for 132 three-row partitions.