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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, openWorld), and the description adds genuinely new behavioral context the schema cannot carry: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint. It does not state failure/error behavior for out-of-range inputs or why n is capped at 18.

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?

The definition and bounded ranges are front-loaded, then examples, then cost and transport details — a sensible order. Three numeric examples is one more than strictly needed for a two-parameter function, a small amount of redundancy but nothing egregious.

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 only two required integer parameters, no output schema, and annotations covering safety, the definition supplies what an agent needs: the computation, valid input ranges, and the payment/transport model. The missing piece is an explicit statement of the return value shape (a single residue) and behavior when n exceeds 18, which is implied but never said.

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 compensate, and it partly does: 'a(n) modulo m' plus the numeric examples make clear that n is the index into the alternating factorial and m is the modulus. However, the stated ranges (n 1–18, m 1–1000000) merely restate the schema's minimum/maximum and give no reason for the n ≤ 18 cap, so the added meaning is thin.

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 names a specific mathematical operation ('the alternating factorial a(n) modulo m') with concrete worked examples, so the agent knows exactly what is computed. It does not, however, differentiate itself from close siblings such as alternating_factorial, alternating_sum, or alternate spellings like alt_factorial, which a reader must infer from the 'mod' suffix.

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 formula and the example inputs (a(5) mod 10, a(6) mod 100) rather than stated: the agent can infer this is the modular form of alternating_factorial. There is no explicit 'use this instead of X' guidance against the many alternating_* siblings, and no statement of what happens outside the stated ranges.

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