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

Beyond the annotations, it discloses the return sentinel (0 for non-octahedral inputs), input domain, price ($0.001 USDC per successful call via x402 on Solana), and an HTTPS endpoint. It does not describe payment failure behavior or rate limits, but annotations already cover read-only/idempotent/non-destructive safety.

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 is compact and front-loads the operation before examples, domain, price, and endpoint. The payment/endpoint sentence is useful for this x402 tool, so little is extraneous, though the first sentence is terse.

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 does explain the returned index or 0 sentinel, and it supplies range, cost, and transport details. However, it leaves 'O(n)' undefined and does not cover error/payment-failure behavior, so it is adequate but not fully complete.

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 explain the sole parameter. It gives the input range and examples showing that the parameter is the value being checked and that the output is its place, but the reuse of 'n' for both the returned index and the schema parameter is potentially confusing, and O(n) remains undefined.

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 defines a specific inverse lookup: given an input, return the n whose octahedral value O(n) equals it, or 0 if absent, with examples mapping 1→1, 6→2, 19→3, 2→0. This is clear enough to distinguish it from octahedral_next/sum, but it never defines 'O(n)' or names the sibling that computes octahedral numbers directly.

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?

The sentinel return and examples imply this is for membership tests or inverse index lookup, but there is no explicit statement of when to use it versus octahedral, octahedral_next, or octahedral_sum. No alternatives or exclusions are given.

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