The formidable looking challenge of quantum TGD is to calculate the M-matrix elements defined by the generalized Feynman diagrams. Zero energy ontology (ZEO) has provided profound understanding about how generalized Feynman diagrams differ from the ordinary ones. The most dramatic prediction is that loop momenta correspond to on mass shall momenta for the two throats of the wormhole contact defining virtual particles: the energies of the energies of on mass shell throats can have both signs in ZEO. This predicts finiteness of Feynman diagrams in the fermionic sector. Even more: the number of Feynman diagrams for a given process is finite if also massless particles receive a small mass by p-adic thermodynamics. The mass would be due to IR cutoff provided by the largest CD (causal diamond) involved.
The basic challenges are following.
The realization that p-adic integrals could be defined if the manifold is symmetric space as the world of classical world (WCW) is proposed to be raises the hope that the WCW integration for Feynman amplitudes could be carried at the general level using Fourier analysis for symmetric spaces. Even more, the possibility to define p-adic intergrals for symmetric spaces suggests that the theory could allow elegant p-adicization. This indeed seems to be the case. It seems that the dream of transforming TGD to a practical calculational machinery does not look non-realistic at all.