I will describe the space of effective field theories consistent with local, unitary, and analytic UV completions, which was termed the EFThedron. Recently the EFThedron was generalized to a non-projective geometry, which can be used to implement new constraints on spectral functions. These include the unitarity bound, which leads to analytic bounds on single Wilson coefficients (instead of bounds only on ratios), or the low spin dominance condition, which drastically reduces the landscape of allowed theories. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]