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

Annotations already cover the read-only/idempotent/non-destructive profile, and the description adds genuinely useful operational context that annotations cannot express: per-call pricing ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint. It does not state failure/modulo-by-zero behavior, which is the remaining gap.

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 clauses: definition, examples, domain bounds, then access/pricing details. Front-loaded with the core semantics and no filler, though the bounds restate the schema.

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 pure function with no output schema, the description supplies examples that reveal the return type (an integer residue), valid domains, and payment/transport requirements. It is essentially sufficient, with only error semantics left unstated.

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 schema alone gives only integer type and bounds with no prose. The description restates the same ranges (redundant with minimum/maximum) but does convey that m is the modulus and n the index through the examples, which is the main value added.

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?

States a specific mathematical operation: the nth octahedral number reduced modulo m, with worked examples. The 'mod m' qualifier clearly separates it from the sibling octahedral/octahedral_sum tools, though it never names them 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 two examples implicitly demonstrate how to call it and the stated ranges define valid input, but there is no explicit guidance on when to pick this over octahedral, octahedral_next, or octahedral_index, nor any note about error behavior for out-of-range inputs.

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