User blog comment:Hyp cos/SCG(n) and some related/@comment-10429372-20140812170828

Nice! How far does you analysis actually go?

I hope you don't mind me posting a bound for SCG(1).

1. triple egde [SVO]

2. triangle [ζ0]

3. loop-edge-double edge-edge-loop [ε(ε0)]

4. edge-double egde-edge-double edge [ε2+ε1]

5. edge-double egde-edge-(edge-loop)(edge-loop) [ε2+ε0^ω]

6. edge-double egde-edge-(ε0*3 graph) [ε2+ε0*3]

7. edge-double egde-edge-edge-(ε0*2+2 graph) [ε2+ε0*2+3]

8. edge-double egde-edge-(ε0*2+2 graph)+stick [f(ε2+ε0*2+2)f1]

9. edge-double egde-edge-(ε0*2+2 graph)+3 dots [f(ε2+ε0*2+2)f0f0f0]

10. edge-double egde-edge-(ε0*2+2 graph)+2 dots [f(ε2+ε0*2+2)f0f0]

11. edge-double egde-edge-(ε0*2+2 graph)+1 dot [f(ε2+ε0*2+2)f0]

12. edge-double egde-edge-(ε0*2+2 graph) [ε2+ε0*2+2]

13. edge-double egde-(ε0*2+2 graph)+7-path [f(ε2+ε0*2+2)f6]

14. edge-double egde-(ε0*2+2 graph)+6-path+stick [f(ε2+ε0*2+2)f5f1]

18. edge-double egde-(ε0*2+2 graph)+6-path [f(ε2+ε0*2+2)f5]

19. edge-double egde-(ε0*2+2 graph)+2 5-paths+3-path [f(ε2+ε0*2+2)f4f4f2]

20. edge-double egde-(ε0*2+2 graph)+2 5-paths+2 sticks [f(ε2+ε0*2+2)f4f4f1f1]

24. edge-double egde-(ε0*2+2 graph)+2 5-paths+1 stick [f(ε2+ε0*2+2)f4f4f1]

34. edge-double egde-(ε0*2+2 graph)+2 5-paths [f(ε2+ε0*2+2)f4f4]

35. edge-double egde-(ε0*2+2 graph)+2 5-paths [f(ε2+ε0*2+2)f4f4]

I had more analysis after this, but I lost it beacause the page suddenly reloaded. But is is fairly obvious after here. The bound I got:

SCG(1) > Hε2ε02ω2+ω4+ω35+ω257(101.18*10 21135 )

I hope you can do even better! (But you get the full credit for this, of course)