Which of the following signifies that no legitimate legal excuse exists?

The breach of contract signifies that no legitimate legal excuse exists because it represents a failure to fulfill the obligations set forth in a legally binding agreement. In legal terms, when a party to a contract does not perform their part as promised, without an acceptable justification, this constitutes a breach. This indicates that the party has not provided a valid legal reason for their noncompliance, opening the possibility for the other party to seek remedies, such as damages or specific performance.

In contrast, the other choices involve actions related to agreements and contracts but do not inherently imply a lack of legitimate excuses. The completion of a task and the signing of an agreement both denote proper adherence to contractual obligations, while the negotiation of terms focuses on discussions and agreement formation rather than the fulfillment or failure of those obligations. Each of these elements is valid within the context of contract law but does not denote unexcused failure like a breach of contract does.