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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds genuinely non-inferable behaviour: the canonical g >= 0 normalisation, rejection of gcd(0,0), the per-call price of $0.001 USDC via x402 on Solana, and an alternate HTTPS endpoint. Only the odd fragment 'Decimals have no leading zeros' is unclear about what output formatting constraint it actually describes.

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 contract before the operational details (rejection, formatting, price, endpoint). The cryptic 'Decimals have no leading zeros' sentence does not clearly earn its place.

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 carries the return contract and does so explicitly (returns g, x, and y, with g >= 0). Pricing and the duplicate HTTPS endpoint round it out; only the non-uniqueness/sign convention of x and y for large inputs is unaddressed.

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 carry the parameters, and it only implicitly establishes that a and b are integers via the g = a*x + b*y identity and the gcd(0,0) rejection. The 201-character digit limit, sign acceptance, and requiredness are left entirely to the JSON schema patterns.

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 a precise verb+resource ('Extended gcd of a and b') and defines the return contract mathematically (g = a*x + b*y, g >= 0), which leaves no ambiguity about what is computed. It does not name or distinguish itself from near-neighbours such as mod_inverse, domb_gcd, or gcd_sum, so a 4 rather than 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 mathematical definition; there is no explicit statement of when to call this versus mod_inverse or gcd_sum. The one concrete boundary given — 'gcd(0, 0) is rejected' — tells the agent a precondition but is not framing guidance.

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