User blog:Bubby3/The Great Googology Todo List

I feel like googolists haven't been doing anything really meaningful or important recently. So here are some things anyone should try to do
 * TON vs SAN or BMS (probally BM2.3), past C(C(W_2*3,0),0). The reason why BMS, is that BMS is most likely way stronger than even DAN.
 * Make guesses for BMS vs TON past C(C(W_2^2,0),0) and a summary of the analysis. (In my guess, it is (0,0,0)(1,1,1)(2,2,1)(3,1,0)(2,0,0))
 * Verify the claim that DAN is (0,0,0)(1,1,1)(2,2,1)(3,0,0)
 * Make a formal anlysis of BMS past pair sequences, or at least one with justifications.
 * Analyze the BMS catching function, between the constant and n+1 or n^2 versions. It is different from OCF array notation fundemental sequnce because of ordinals like (0,0,0)(1,1,1)(1,1,0)(2,2,1), which has an offset. Expalned in this blog post (coming soon).
 * Analyze stronger proof theores up to second-order arthemic and even beyond, and see with Pi-n reflection mathess the stronger or weaker guess. Use SAN or BMS for the comparisons.
 * Make a working version of second generation SAN, because the two versions made don't work.