In program-based harness generation, every program that parses cleanly without syntax errors belongs to the protocol-compliant harness space \mathcal{H}_\Pi.

Identify which formal space the candidate program succeeded in entering, which formal space it failed to enter, and state the exact formal condition that prevented its entry.

Which issues specifically prevent a protocol-compliant harness in $\mathcal{H}_\Pi$ from qualifying for the executable harness subset ($\mathcal{H}_\Pi^{\text{exec}}$)?

Order the nested formal harness spaces from broadest superset to most restrictive subset.

Protocol-compliant harnesses in $\mathcal{H}_\Pi^{\text{exec}}$ must run successfully without runtime exceptions, tool-call failures, or interface crashes under an environment ___.

Analyze the formal distinction between protocol compliance ($\mathcal{H}_\Pi$) and execution success ($\mathcal{H}_\Pi^{\text{exec}}$). Explain why full adherence to protocol $\Pi$ does not guarantee inclusion in the executable harness subset.

Match each verification failure condition to the formal space boundary it directly prevents a candidate harness from crossing.

Based on the formal nested spaces framework, identify the most restrictive space the candidate harness achieved, explain why it cannot enter the subsequent space, and specify the operational requirement needed for advancement.

The raw generation space $\mathcal{G}$ represents an unrestricted set of programs emitted by a generative model that contains the syntactically valid harness space $\mathcal{H}^{\text{syn}}$ as a subset.

Which formal harness space encompasses the entire unrestricted output of programs generated by a model prior to any syntactic or protocol filtering?

Outline the three successive containment filters that progressively narrow the raw generation space $\mathcal{G}$ down to the executable harness subset $\mathcal{H}_\Pi^{\text{exec}}$ in the nested relation $\mathcal{G} \supseteq \mathcal{H}^{\text{syn}} \supseteq \mathcal{H}_\Pi \supseteq \mathcal{H}_\Pi^{\text{exec}}$.

In program-based harness generation, candidate harnesses are evaluated within nested formal spaces beginning with the unrestricted output space of programs known as the ___ generation space.

According to protocol $\Pi$, what four specifications are established for (M, P, A, F)?

Explain why a candidate harness in the syntactically valid space $\mathcal{H}^{\text{syn}}$ is not guaranteed to belong to the protocol-compliant space $\mathcal{H}_\Pi$, contrasting syntax validity with protocol $\Pi$ requirements.

Match each formal harness space to its corresponding description.