Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Johnson-Lindenstrauss Flattening Conjecture

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of $\mathit{\text{[arXiv:}}\mathit{\text{2207.12799.v1]}}$. For the sake of wide accessibility we give a self-contained treatment of them.