@CWcx I've uploaded the charts at dec41.user.srcf.net/exp/tmf_rp/tmf_rp.pdf with some descriptions.

(for the adams spectral sequence of tmf ∧ RP^∞)

Hey Thanks! These look really awesome! I'm excited to look through them

For what spaces X (and any coefficients k) is the cohomology ring of the free loop space X^{S^1} known concretely in terms of generators and relations?