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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so the safety profile is covered. The description adds genuinely new behavioral context the annotations do not: a per-call price ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint, which matters for payment/auth decisions. It stops short of describing the return value, though for a scalar math function that is near-obvious.

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 definition and combinatorial meaning are front-loaded, followed by examples and then operational details (range, price, HTTPS alternative). Every sentence is useful, though the pricing/URL sentence is dense and could be set apart more cleanly.

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 two-parameter scalar function with no output schema, the description covers definition, interpretation, examples, input range, cost, and a transport alternative. The only material gap is the k bound, which the input schema supplies, so the definition is effectively complete for correct invocation.

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 carry the semantic burden, and it does: it explains n and k through the permutation/cycle interpretation and gives concrete outputs (c(5,2)=50, c(5,1)=24). It states n's range (0–64) but omits k's range, which is only recoverable from the schema bounds.

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 precisely defines the resource: the unsigned Stirling number of the first kind, stated as the absolute value of s(n,k), with the combinatorial interpretation (permutations of n with k cycles). The 'unsigned/absolute value' framing implicitly distinguishes it from the signed stirling1 sibling, but it never names stirling1, stirling1_row, or stirling1_rec explicitly, so sibling differentiation is only implicit.

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?

Usage is only implied: calling it yields a single c(n,k). The description gives worked examples and the n domain but offers no explicit guidance on when to pick this over stirling1 (signed), stirling1_row (a whole row), or stirling1_rec despite those siblings being present. Additions like 'use stirling1_row for a full row' would raise this score.

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