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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint and destructiveHint=false, so safety is covered. The description adds materially useful non-schema context: it costs $0.001 USDC per successful call, is billed via x402 on Solana, and has a mirror HTTPS endpoint at a named URL — exactly the kind of operational detail an agent needs before invoking a paid tool.

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?

Four sentences, front-loaded with the operation, then worked examples, then the domain bound, then pricing/transport. Each sentence carries distinct information; the pricing and endpoint lines take space but are justified for a metered tool.

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 single-integer read-only math tool with no output schema, the description supplies the critical missing piece — the return type ('reduced fraction') and concrete example values — so the agent knows to expect something like '5/3' rather than a float. Only the numerical convention edge case (whether B1 is +1/2) is implied by examples rather than stated outright.

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 coverage is 0%, so the description must carry the parameter. It does: 'sum of B0 through Bn' defines what n indexes, and 'n runs from 0 to 40' restates and contextualizes the schema's min/max. The only gap is not stating the type/error behavior for out-of-range or non-integer input.

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?

States a specific verb+resource: the cumulative sum of Bernoulli numbers B0 through Bn, returned as a reduced fraction. It even pins the Bernoulli convention by giving worked results (B1 sum = 3/2, B2 sum = 5/3), which distinguishes it semantically from the sibling `bernoulli` and `bernoulli_denom`. It stops short of naming those siblings explicitly, so it is not a clean 5.

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 or when-not guidance, and no reference to the obvious alternatives `bernoulli` (single number) and `bernoulli_denom` (denominator). The agent must infer from the tool name alone that this returns a running cumulative sum rather than an individual term.

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