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

Annotations already cover read-only/idempotent/non-destructive, so the bar is lower; the description adds real value beyond them by disclosing the return-type shift past 15 digits (decimal string), the per-call price, and an HTTPS alternative endpoint. It does not discuss error behavior when lo > hi, which is the one remaining behavioral gap.

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 core operation, then constraints, return format, pricing, and transport in short declarative sentences. Each sentence carries a distinct fact; only the example value is arguably optional padding, but it disambiguates indexing.

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 math tool with no output schema and no parameter descriptions, the definition supplies domain bounds, ordering constraint, indexing base, output-type caveat, and cost/transport details — everything needed to call it correctly and predict the response shape.

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: both parameters are named, their inclusive-range relationship is defined, the lo<=hi constraint is stated, and the 0..80 domain is repeated (duplicating the schema's min/max but necessary at 0% coverage). The example clarifies 0-based indexing.

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 with scope: the SUM of Riordan numbers over the inclusive range lo..hi. The range framing implicitly distinguishes it from the single-value sibling 'riordan' and the modular sibling 'riordan_mod', plus the worked example (R(0)..R(10)=989) pins the indexing convention.

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?

Gives validity conditions ('lo must not pass hi', indices 0..80) and a worked example, so usage is implied clearly, but it never names an alternative tool or states when to prefer this over 'riordan' or 'riordan_mod'. No exclusions or negative guidance.

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