x402-is-deficient-number
Is Deficient Number: Returns true when the value's proper divisors sum to less than the value 🆓 5 free trial calls per signed wallet
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| value | No |
Is Deficient Number: Returns true when the value's proper divisors sum to less than the value 🆓 5 free trial calls per signed wallet
| Name | Required | Description | Default |
|---|---|---|---|
| value | No |
Changes observed during successful MCP inspections.
Input schema / properties / value / descriptionRemoved value: -"Value to process"Input schema / properties / valueAdded value: +{
+ "description": "Value to process",
+ "type": "string"
+}Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are supplied, so the description carries the full burden. It does disclose the exact boolean semantics (true when proper divisors sum to less than the value), which is genuinely useful, but says nothing about accepted input domain (negatives, zero, non-integers, very large values) or error behavior.
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 sentence is tight and front-loaded, but the trailing '🆓 5 free trial calls per signed wallet' is promotional noise that does not help an agent invoke the tool.
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 single-parameter boolean predicate with no output schema and no annotations, defining the truth condition covers the main gap. Missing input-domain constraints and sibling disambiguation keep it from being complete.
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?
One parameter named 'value' with 0% schema description coverage, so the description must compensate. It implies an integer via 'proper divisors' but never states the accepted range, format, or whether strings with non-digits are rejected.
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 predicate and defines it in the same sentence: true when the sum of proper divisors is less than the value. An agent can tell it apart from the many unrelated siblings, though it does not distinguish itself from near-duplicate siblings like x402-is-deficient or x402-is-deficient-num.
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?
No guidance on when to use this instead of the many overlapping alternatives (x402-is-deficient, x402-is-deficient-num, x402-deficient-numbers). The '5 free trial calls' promo also muddies whether this is a paid/free tier decision.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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