On rectangular Toda brackets and Oda's extension problems

This paper tackles \textit{N. Oda}'s extension problems for the homotopy groups $π_{39}(S^{6})$, $π_{40}(S^{7})$, and $π_{41}(S^{8})$ localized at 2, the issues having eluded resolution for more than four decades. We introduce a tool for the theory of determinations of unstable homotopy groups, name