Magnon BEC as an Effective Regime of θ-Network Consistency: a TMDD Framing

I show that the kinetic equation (KE) for magnon Bose--Einstein condensation reported in F. Kühn et al., Enhancement of magnon flux toward a Bose--Einstein condensate (Phys. Rev. B, 2024), can be recovered as an effective description within the Tensor Model of Discrete Dynamics (TMDD). In this framing, external pumping, thermalization and cascade behavior are not postulated as separate ingredients but arise from a single variational principle of informational consistency in a θ-network. The observed transition from Kolmogorov-Zakharov cascade to kinetic instability (KI) is reproduced as a switch between dominant terms in the TMDD action functional, while the stationary BEC density and its linear dependence on pump power follow from the network's self-calibration and informational volume constraint.