I won't spoil it for you, but you could find out that you might want to phrase that question of yours differently..
I don't think there's much understanding to be gained by attaching sliders with vague, underspecified labels to a graph.
And on the breakthrough technology question: of course we could discover a unknown technology that will instantly solve everything without even having to honor the inertia of the slow but hard to steer forces that make up climate change. And while I really hope this would happen, I'd rather have more realistic scenarios in the meantime.
Suppose we invent free energy. How long will it take for that technology to replace everything on the planet? How much emissions will this distribution of technology produce? Even with fairytale-style-technology overcoming the inertia of the ongoing processes will be anything but easy.
https://www.climateinteractive.org/tools/en-roads/the-en-roa...
https://www.climateinteractive.org/tools/climate-action-simu...