User blog:Wythagoras/New bound for SSCG(2)

I have discoverd a new bound for SSCG(2).

SSCG(2) > \(2 \uparrow\uparrow 2 \uparrow\uparrow 18 \)

I use Gn for a graph that may contain n vertices.

First graphs:



G12: 2x Graph 2 + 1x Graph 1 + 1 dot

G13: 2x Graph 2 + 1x Graph 1

G14: 2x Graph 2 + 3 sticks

G15: 2x Graph 2 + 2 sticks + 3 dots

G18: 2x Graph 2 + 2 sticks

G19: 2x Graph 2 + 1 stick + 9 dots

G28: 2x Graph 2 + 1 stick

G29: 2x Graph 2 + 21 dots

G50: 2x Graph 2

G51: Graph 2 + 16x Graph 1 + 1 sticks

G52: Graph 2 + 16x Graph 1 + 3 dots

G55: Graph 2 + 16x Graph 1

G56: Graph 2 + 15x Graph 1 + 3 sticks + 1 dot

G57: Graph 2 + 15x Graph 1 + 3 sticks

G58: Graph 2 + 15x Graph 1 + 2 sticks + 5 dots

G63: Graph 2 + 15x Graph 1 + 2 sticks

G64: Graph 2 + 15x Graph 1 + 1 stick + 13 dots

G77: Graph 2 + 15x Graph 1 + 1 stick

G78: Graph 2 + 15x Graph 1 + 29 dots

G107: Graph 2 + 15x Graph 1

Now it gets bigger...
G108: Graph 2 + 14x Graph 1 + 31 sticks

G108+ \(3*2^{2} - 2 - 6\) = G112 = Graph 2 + 14x Graph 1 + 30 sticks

G108+ \(3*2^{3} - 4 - 6\) = G122 = Graph 2 + 14x Graph 1 + 29 sticks

G108+ \(3*2^{4} - 6 - 6\) = G144 = Graph 2 + 14x Graph 1 + 28 sticks

G108+ \(3*2^{5} - 8 - 6\) = G190 = Graph 2 + 14x Graph 1 + 27 sticks

...

G108+ \(3*2^{32} - 62 - 6\) = G12884901928 = Graph 2 + 14x Graph 1

Beyond Goucher's bound
The 'Graph 1' function

G12884901928 = Graph 2 + 14x Graph 1

G12884901929 = Graph 2 + 13x Graph 1 + 644245094 sticks

G \(3*2^{644245095} + 37\)  = Graph 2 + 13x Graph 1

G approx. \(3*2^{3*2^{644245095}}\)  = Graph 2 + 12x Graph 1

G approx. \(3*2^{3*2^{3*2^{644245095}}}\)  = Graph 2 + 11x Graph 1

G approx. \(3*2^{3*2^{3*2^{3*2^{644245095}}}}\)  = Graph 2 + 10x Graph 1

G approx. \(2 \uparrow\uparrow 18 \) = Graph 2

G approx. \(2 \uparrow\uparrow 18 \) = \(2 \uparrow\uparrow 18 \) x Graph 1

SSCG(2) > \(2 \uparrow\uparrow 2 \uparrow\uparrow 18 \)