Quantum Modularity of Mock Theta Functions from the Alpha Hierarchy

This is Part 2 of 1. We study the radial limits of the mock theta functions Mₖ (τ) constructed from the alpha hierarchy introduced in 1. For k=1 we compute these limits numerically at roots of unity and show they satisfy quantum modular transformation properties in the sense of Zagier. The difference L₁ (-1) -L₁ (1) is observed to equal π²/30 - i/144 plus higher terms involving π⁴, π⁶ and odd zeta values ζ (3), ζ (5), ζ (7),. . . with rational coefficients matching those of the Lambda functions Λₖ from 1. This provides numerical evidence that the functions Mₖ (τ) give rise to quantum modular forms whose special values involve π² and odd zeta values in a structured way. Conjectures are stated for general k. 1 Hussain, M. R. (2026). Alpha Functions: A New Hierarchy with Connections to Elliptic Integrals and Mock Theta Functions. Zenodo. DOI: 10. 5281/zenodo. 19025728