a demonstration of the successful exploitation of the vulnerability without providing a semi or fully automated attack program (i

a small-scale test or prototype demonstration that takes some new idea and subjects it to some stress-testing by reality -- not a full dose but enough to show that the idea might be worth pursuing

Creating a product limited in functionality to be sure that the technology will perform as required. When new technology is involved, or a novel interaction is proposed, this may be used as a risk mitigation tactic.

The development of a legitimate application which proves the workability of a proposed hardware or software solution.

A prototype that's built to show that the technique, system design, or marketability of a proposed application or system is likely to be as good as expected.

A demonstration of feasibility.

Proof of concept is a short and/or incomplete realization (or synopsis) of a certain method or idea(s) to demonstrate its feasibility, or a demonstration in principle, whose purpose is to verify that some concept or theory is probably capable of exploitation in a useful manner.

Product has been proven to work through analysis of the science.