bertrand_postulate_verify

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

No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool does without describing how it behaves: it does not mention whether it returns a boolean, a proof, or an error for invalid inputs; it does not discuss computational limits, performance, or side effects. This leaves critical behavioral aspects unspecified.

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 extremely concise and front-loaded: the first sentence directly states the tool's purpose, and the second provides domain/category context without unnecessary elaboration. Every word serves a clear purpose, making it efficient and easy to parse.

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 complexity of verifying a mathematical postulate, the description is insufficient. There are no annotations, no output schema, and the input parameter is undocumented. The description does not explain what the tool returns or how it handles edge cases, leaving significant gaps for an AI agent to understand and use the tool effectively.

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 input schema has 0% description coverage, and the description does not add any parameter semantics. It mentions 'given n' but does not explain what n represents (e.g., an integer greater than 1), its valid range, or how it is used in verifying the postulate. This fails to compensate for the lack of schema documentation.

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 clearly states the tool's purpose: 'Verify Bertrand's postulate for given n.' It specifies the verb ('verify'), the mathematical concept ('Bertrand's postulate'), and the required input ('given n'). However, it does not explicitly differentiate from sibling tools, as there are no obvious alternatives for verifying this specific postulate in the list.

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?

The description provides minimal guidance: it mentions the domain ('arithmetic') and category ('prime_conjectures'), which implies usage in mathematical contexts. However, it does not specify when to use this tool versus alternatives (e.g., general prime-checking tools like 'is_prime'), nor does it outline prerequisites or constraints (e.g., valid ranges for n).

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