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

With no annotations, the description carries the full burden. It does disclose the return semantics (x modulo the product of moduli) and mentions the payment model (5 free trial calls per signed wallet), which is useful business context. However, it omits important behavioral facts for CRT such as what happens with non-coprime moduli or unsolvable systems.

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 core explanation is a single front-loaded sentence with no wasted clauses. The trailing '🆓 5 free trial calls per signed wallet' promotional tag is minor noise that doesn't earn its place in a functional description.

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 four-parameter tool with zero schema descriptions, no annotations, and no output schema, the description leaves too much unspecified: parameter formats, the required-field ambiguity, and the coprimality assumption are all unaddressed. It is not adequate for correct invocation.

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% across four parameters, and the description only obliquely references 'remainders and moduli arrays'. It never explains the redundant 'a'/'m' versus 'moduli'/'remainders' pair, whether values are comma-separated or JSON in a string, or which fields are required (none are marked required).

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 mathematical resource ('solves a system of congruences') and even names the return value ('x modulo the product of moduli'), so an agent knows exactly what computation happens. It falls short of 5 only because the mention of 'remainders and moduli arrays' doesn't map cleanly onto the four schema parameters, leaving the input shape slightly ambiguous.

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 when-to-use, when-not-to-use, or alternative guidance. The description implies the domain (solving congruence systems) but never tells the agent when this tool beats alternatives like extended-gcd or multiplicative-inverse, nor which of the two parameter pairs to supply.

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