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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It says nothing about whether p must be an odd prime, what the returned values (-1, 0, 1) mean, or error conditions for invalid inputs.

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?

It is short, but it is under-specification rather than conciseness: one duplicated phrase and no content. Nothing is front-loaded because there is nothing to load.

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?

For a mathematical tool with zero annotation coverage, no output schema, and placeholder parameter docs, the description is completely inadequate. An agent cannot determine input validity rules or the meaning of the result.

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?

Schema description coverage is nominally 100%, so the baseline of 3 applies per the rubric. However, the schema text is placeholder ('A to process', 'P to process') and the description adds no meaning such as a must be an integer and p an odd prime, so the actual semantic value is near zero.

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?

The description is the tautology 'Legendre Symbol: Legendre Symbol', restating the tool name twice with no verb, no statement of what is computed, and no distinction from siblings like x402-is-quadratic-residue or x402-jacobi. The name alone hints at a math operation, but the description itself adds nothing.

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?

No guidance whatsoever on when to use this versus the many other number-theory siblings (is-quadratic-residue, euler-phi, prime-factors). No prerequisites, no input constraints, no alternatives named.

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