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

Annotations already cover readOnly/idempotent/non-destructive/openWorld, yet the description adds genuinely new behavioral facts: the return type flips to a decimal string past 15 digits, and each successful call costs $0.001 USDC via x402 on Solana. Payment and output-shape disclosure go well beyond the annotation set; only error behavior (e.g. what happens if lo > hi) is left unstated.

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?

Front-loaded with the definition, then constraints, then output format, then price and endpoint. Every sentence carries information an agent needs (bounds, relationship, return type, cost). The pricing/HTTPS sentence is somewhat boilerplate across this server's tools but is relevant to invocation cost.

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-integer, annotation-covered, read-only computation with no output schema, the definition supplies domain bounds, the lo<=hi invariant, inclusive semantics, return-type behavior at the 15-digit threshold, and cost. The only real omission is failure behavior when lo > hi.

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 load, and it does: 'lo must not pass hi' expresses the cross-parameter invariant the schema cannot, 'each index runs from 0 to 20' names the domain, and the inclusive bound is confirmed by the a(0)..a(5) example. It never explains why lo/hi matter beyond range, but that is the whole semantic content here.

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 and resource with scope: 'sum of Fubini numbers from lo through hi inclusive', plus a worked example (a(0)..a(5) = 634) that pins down exactly what is summed. It is clear on its own, but never names the sibling `fubini` (single term) or `fubini_mod`, so an agent must infer the distinction from the names alone.

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 gives the operative constraints ('lo must not pass hi', indices 0-20) which implicitly tell the agent when a call is valid, but there is no explicit guidance on when to pick this over `fubini` or `fubini_mod`. Usage is implied by the name contrast rather than stated.

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