"Step-up equity."
Self-funded searchers use this term erroneously. They claim that if you inject 100% of the equity, your equity is stepped up to own maybe 40% of the target company. Stop calling it a step-up - if anything it should be called step-down equity.
The original step-up terminology exists in the traditional search fund model. Investors who fund a search (high risk) get to roll that investment into a deal at a discounted valuation if and when a deal closes. The discount is the step-up.