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

Annotations already declare readOnly, idempotent, non-destructive and openWorld, so the safety profile is covered. The description adds genuinely new behavioral context: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint. It stops short of describing what happens on the terminal permutation, which is the remaining behavioral unknown.

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 an example, then the boundary note, then payment/transport details — a sensible ordering. Every sentence is short and relevant, though the HTTPS endpoint line is operational metadata rather than tool semantics.

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 must carry return-value semantics, and it only does so via example; it never says whether the result is the array itself, a wrapped object, or an error/null when no successor exists. For a one-parameter deterministic utility the gap is small but real, especially at the terminal permutation.

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%, and the single 'perm' parameter's constraints (integers 0-9, max 10 items, presumably distinct elements) are documented nowhere. The examples implicitly convey the input shape (an array of small integers that is a permutation), which is some compensation, but length and value limits and the distinctness requirement are left to inference.

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 states a precise operation ('next permutation in lexicographic order') and reinforces it with a concrete example pair, so an agent immediately knows the transform. It never names or distinguishes itself from close siblings like perm_rank, perm_inverse or perm_compose, which keeps it short of a 5.

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 only implied by the worked example; there is no explicit statement like 'use this to iterate permutations' or pointer to perm_rank/perm_inverse for other needs. The one edge case mentioned (the descending permutation has no successor) hints at a boundary condition but doesn't say what the tool returns or errors in that case.

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