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

With no annotations, the description carries the full behavioral burden. It usefully discloses the underlying algorithm and a pricing/rate-limit fact ('5 free trial calls per signed wallet'), which is real behavioral context. However it says nothing about the return value, input type coercion, or errors for non-numeric input.

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?

One front-loaded sentence covering purpose and method, plus a short actionable pricing note. Tight and waste-free, though the emoji promo line is mild noise.

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 simple one-parameter predicate with no output schema, the description covers what the tool computes but omits the return contract (boolean?), input format constraints, and any routing guidance among the large family of sibling predicates. Adequate but with clear gaps.

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% for the single 'value' parameter. The description references 'value' and the test implicitly assumes an integer, but the schema types it as a string and nothing clarifies accepted format (decimals, negatives, non-numeric strings). Helps partially but does not compensate for the coverage 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?

States a specific verb and resource: 'Checks whether value is a hexagonal number', and even names the mathematical test used (1 + 8n perfect-square). This is unambiguous on its own, though it never differentiates itself from the many sibling predicates (is-pentagonal, is-octagonal, is-triangular, etc.).

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?

There is no guidance on when to use this versus the dozens of other is-* number checks, no exclusions, and no mention of alternatives. Usage is only inferable from the tool name itself.

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