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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: not the return shape (boolean vs. symbol vs. error), not handling of non-prime p, not edge cases like a=0 or negative a. For a no-annotation tool this is a complete gap.

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 the brevity comes from under-specification rather than economy: the same phrase is repeated twice and no information is front-loaded. There is nothing to trim, but also nothing that earns its place.

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?

There is no output schema and no annotations, so the description is the only channel for meaning, and it supplies none — not the return convention, not domain constraints on p. Only the trivial two-parameter schema keeps this from being a 1.

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 100%, so the two parameters are formally documented, and the rubric sets a baseline of 3 in that case. However, the placeholder text ('A to process', 'P to process') conveys no mathematical meaning — the description adds nothing about expected domains (p prime, a integer) to compensate.

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 tool name restated twice ('Is Quadratic Residue: Is Quadratic Residue'), which is tautological rather than explanatory. It never states that it determines whether an integer a is a quadratic residue modulo p, nor does it distinguish itself from the sibling 'x402-legendre-symbol' (the underlying computation).

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 when-to-use context, no prerequisites (e.g. p must be prime), and no mention of the closely related legendre-symbol or other number-theory predicate tools. The agent is left to infer application entirely from the name.

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