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

Annotations already cover read-only/idempotent safety, and the description adds genuinely non-structural context: the a+b ≤ 8192 cap on the composed result, a per-call price of $0.001 USDC paid via x402 on Solana, and an HTTPS alternative endpoint. Payment/auth requirements are exactly the kind of thing annotations cannot convey. It stops short of saying what the response looks like.

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?

Four short sentences, front-loaded with the mathematical meaning, then the constraint, then cost and transport. Payment and endpoint details are necessary but slightly interrupt the math narrative.

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?

For a two-integer, no-output-schema tool this is nearly complete: inputs, constraint, cost, and alternate transport are all covered. The one missing piece is what the call returns (presumably the unit at index a+b), which the absent output schema leaves undocumented.

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 burden, and it does: 'a' and 'b' are identified as unit indices whose sum is the output index, and the combined bound is stated. It does not explain the minimum-side (0) or clarify indexing conventions/edge cases like a=0, leaving a small gap.

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?

Specific verb + resource: 'Compose two solutions of x^2 - 2y^2 = ±1' with the group-law semantics spelled out (unit(a) * unit(b) = unit(a+b)). That distinguishes it from siblings like pell, pell_sum, and neg_pell, though it never names those siblings explicitly.

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 operation and its operand constraint (a+b ≤ 8192) are stated, which implies when the tool applies, but there is no explicit guidance on when to pick this over pell, pell_sum, or neg_pell, and no mention of when it would fail or be inappropriate beyond the index bound.

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