Conjecture relations (Ramanujan Machine)

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

No annotations are provided, so the description bears full responsibility. It discloses key behaviors: numerical verification to >=25 digits, results are conjectured (provenance 'conjectured_relation'), and highlights the non-proven nature. It also hints at computational cost via parameter description. While it lacks details on side effects or resource usage, the disclosure is substantial for a numeric computation tool.

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 description is extremely concise: two sentences with a brief parameter list at the end. Every word is informative, front-loading purpose, method, and usage condition. No waste.

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?

Given the tool's complexity (algorithmic search, numerical verification, conjecture status) and the presence of an output schema, the description covers when to use, what it does, parameter guidance, and key limitations. It is complete for an AI agent to select and invoke correctly.

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?

With 100% schema coverage, baseline is 3. The description adds meaningful context: 'MANY digits' for value, 'cost grows fast' for max_terms, and default values. It also notes that the search needs >16 digits, which is not in the schema. This enhances usability beyond the schema alone.

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 clearly states the tool conjectures relations for real constants using PSLQ and continued-fraction search, explicitly distinguishing it from identify_constant by specifying usage when 'identify_constant returns UNIDENTIFIED'. The verb 'conjecture' and resource 'relation for a real constant' are specific, and the unique method is highlighted.

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 description explicitly says 'Use when identify_constant returns UNIDENTIFIED', providing a clear usage condition. It does not list all alternatives, but this direct reference to a sibling tool gives strong guidance. The mention of 'NOT proved' implies when not to use (when proven relations are needed).

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