Execute a mathematical capability

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Goes far beyond the sparse annotations (all false): discloses that 'COMPLETED does not by itself establish a mathematical conclusion', explains the exact scoping limits of invocation, describes the default view's projection and mcp_projection reporting, and details timeout/retry semantics. This is rich behavioral context with no contradiction.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is long but every sentence adds essential operational detail. It is front-loaded with the purpose, and the later sections systematically cover invocation protocol, verification semantics, view options, timeouts, and examples. Minor redundancy between 'One invocation covers only its exact supplied input or claim' and 'Repeating finite or bounded instances does not widen that scope' but not enough to penalize heavily.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the output schema exists, the description appropriately focuses on invocation behavior rather than return values. It covers prerequisites (describe first), mode/view selection, timeout/retry policy, scope limitations, and post-invocation inspection guidance. The examples make the envelope structure crystal clear for a complex tool.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema has 0% description coverage, but the description compensates fully: it explains mode ('Use EXPLORE for proposed, heuristic, or computed evidence and VERIFY only for an installed checker-backed contract'), view behavior and when to use each variant, and provides concrete payload examples for both capability_id and payload structure, making the free-form payload meaningful.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

Opens with a specific verb+resource: 'Execute one installed mathematical capability' and immediately differentiates by requiring 'capability.describe first'. This clearly distinguishes it from the sibling describe tool and names the exact action and target.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly instructs to 'Call capability.describe first; do not guess payload fields or aliases.' It prescribes when to use EXPLORE vs VERIFY, when to use SUMMARY/FULL views, and even advises partitioning larger searches due to the 150-second timeout. This is strong alternative-aware guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.