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

Annotations already cover read-only, idempotent and non-destructive semantics, so the description's added value is the return-type threshold ('past 15 digits the value is a decimal string') and the per-call price under x402 on Solana — genuinely useful behavior an agent cannot get from the schema. The n-range restates the schema bounds, and it does not say whether failures are still charged.

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 formula and examples, then constraints, then output format, then pricing/transport — a sensible order with no filler. The pricing and URL sentence is marketing-adjacent but still decision-relevant for a paid x402 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?

With no output schema, the description steps in with the output-format rule, so an agent knows to expect either a number or a decimal string. For a single-integer-input, single-value-output tool this is essentially complete, though the cost-on-failure and sibling relationship remain unstated.

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 load, and it does: n is defined as the index into the alternating-factorial sequence with range 1–200 and concrete example values that let an agent sanity-check its input. It stops short of describing edge behavior such as non-integer or out-of-range input rejection.

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 gives the exact recursive-formula definition, worked examples (af(1)=1, af(3)=5, af(4)=19), and the domain of n, so an agent knows precisely what is computed. It does not, however, distinguish itself from the near-identically named sibling alternating_factorial (and alt_sum/alternating_sum), which is a real disambiguation gap in this catalog.

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 mathematical definition and the documented range, but there is no explicit 'use this when' or 'prefer X instead' guidance, and the obvious sibling alternating_factorial is never mentioned. The HTTPS endpoint note is a transport alternative, not a tool-selection guideline.

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