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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is covered. The description adds valuable behavior beyond annotations: the pricing model ($0.001 USDC per successful call via x402 on Solana), the HTTPS endpoint, and the fact that results past 15 digits are returned as a decimal string. It does not describe error behavior, but the added payment and output-format context is meaningful.

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 front-loaded with the core mathematical definition, followed by examples, domain bounds, return-format caveat, and payment details. It is mostly efficient, though repeating the schema's min/max bounds is somewhat redundant. Every sentence still carries useful information for invocation.

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, so the description appropriately discloses that results exceeding 15 digits are returned as a decimal string. It also covers payment requirements and an alternate HTTPS endpoint. For a two-parameter math tool, this is nearly complete, with only minor gaps around error behavior and fuller parameter definitions.

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 0%, so the description must compensate for bare parameter types. It gives the valid ranges for n and x (which duplicate schema min/max) and clarifies semantics through examples like T(0,x)=1 and T(1,x)=x, but it does not explicitly define n as the polynomial degree and x as the evaluation point in prose. The compensation is partial.

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 states a specific mathematical operation: the Chebyshev polynomial of the first kind T(n,x) evaluated at integer x. It distinguishes itself from sibling tools such as chebyshev_u by explicitly naming 'first kind' and provides a concrete example T(2,3)=17. An agent can identify the operation without ambiguity.

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 implies when to use the tool (computing T(n,x)) through examples and domain bounds, but it does not explicitly say when to choose it over siblings like chebyshev_u, chebyshev_disc, chebyshev_prod, or chebyshev_rec. No exclusions or alternative-routing guidance are given.

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