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

Annotations already declare readOnly, idempotent, non-destructive, which fits a pure computation. The description adds genuine behavioral context beyond them: exact output formatting, worked examples with ending '0' invariant, the accepted input range, per-call pricing ($0.001 USDC via x402 on Solana), and an alternate HTTPS endpoint. That payment/endpoint detail is material to invocation.

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 output format and examples, then range, then pricing and endpoint. Every sentence is relevant; the pricing/endpoint sentence is slightly tangential but necessary for a paid x402 tool. No filler.

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?

With no output schema and no parameter descriptions, the description fully shoulders format and range disclosure, giving the exact string format and examples. Pricing and alternate transport close the loop. Nothing essential for a correct call is missing.

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 meaning and it largely does: 'n runs from 0 to 999999999999999' mirrors the schema bounds, and the examples show what each n maps to. It still doesn't clarify failure behavior for out-of-range input, but the semantics of the single parameter are well conveyed.

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: it emits the factorial-base (factoradic) digits of n, comma-separated, highest place to 0!. Concrete examples ('23 is "3,2,1,0"') remove ambiguity. However it does not distinguish itself from siblings like factoradic_decode, factoradic_digit, factoradic_length, or factoradic_sum, which an agent must infer.

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 implied by the examples (convert an integer to its factoradic digit string), but there is no explicit when-to-use guidance and no routing to the many sibling factoradic tools. The advertised range and price hints at what kind of calls are valid, but not when this beats factoradic_digit or factoradic_length.

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