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

Annotations already cover read-only, idempotent, open-world, and non-destructive traits, and the description adds genuinely useful context beyond them: the exact cost ($0.001 USDC per successful call via x402 on Solana) and an alternative HTTPS endpoint. It also reveals sample return values (bit 0=0, bit 1=1, first 8 bits 01000101), compensating for the absent output schema.

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?

It is front-loaded with the core definition, then examples, then the domain bound, then cost and endpoint details. Dense but each element serves a purpose; minor redundancy between the max value in prose and schema is negligible.

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 compensates by giving multiple concrete bit values, and annotations handle the safety profile while pricing and the HTTPS alternative round out the call contract. Nothing critical for correct invocation is missing.

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 parameter meaning. It states the parameter is a 0-based index and gives the valid range, which adds semantic clarity over the bare integer type in the schema, but it does not elaborate beyond that for the single parameter.

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 mathematical definition of the value (parity of the exponent of 2 in n+1) and concrete examples, so an agent knows exactly what is computed. However, it does not differentiate the tool from its close siblings period_double_prefix and period_double_sum, which an agent would likely confuse.

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 statement of when to use this tool versus the prefix or sum siblings, and no exclusions or prerequisites. The definition and domain constraint are present, but selection guidance between the three period_double tools is left entirely to inference.

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