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

Annotations already declare readOnly/idempotent/non-destructive/openWorld, so the safety profile is covered by structured data. The description still adds real context beyond them: non-representable n is 'rejected', n is bounded to 0..10^12, and the call is billed $0.001 USDC per *successful* call via x402 on Solana. It does not say what a rejection looks like (error vs. null).

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 front-loaded, then examples, then the rejection edge case, then range and price. Each sentence carries information. The opening sentence is slightly dense/grammatically awkward as a lead, but there is no filler.

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 should say what comes back for a successful call — the pair (x, y) is only implied by 'choosing the greatest y', and the shape of the rejected case is undefined. Range, pricing and endpoint are covered, so the gap is confined to return/failure semantics.

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 carries the burden. It does define what n means semantically (the integer to be written as a sum of two squares) and repeats the same 0..10^12 bound already in the schema's minimum/maximum. That is minimal compensation — no notes on precision, large-input behavior, or performance implications.

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 an explicit mathematical definition (x <= y, x^2 + y^2 = n) plus the tiebreak rule 'choosing the greatest y' and two worked examples (5 → 1,2; 25 → 0,5). That is far more specific than the name alone. It stops short of naming the sibling two_squares/all-pairs variant, so the agent must infer the distinction rather than being told.

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 context is implied by the domain (give a perfect-square-sum target, get one canonical pair) and the input range is stated, but there is no explicit guidance on when to pick this over two_squares, three_squares or four_squares. The HTTPS alternative is documented, which is useful, but that is an access-path note rather than a use-case rule.

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