ScorpTech x402 Tools

Central Sum

central_sum

Read-onlyIdempotent

The sum of central binomial coefficients from lo through hi. The sum from C(0) through C(5) is 351. lo must not pass hi. Each index runs from 0 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-sum

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "lo": "<lo>",
      "hi": "<hi>"
    },
    "name": "central_sum"
  }
}

Input Schema

Name	Required	Description	Default
`hi`	Yes
`lo`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.6/5.0

Behavior4/5

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

Annotations already cover read-only/idempotent/openWorld, but the description adds real behavioral context not available elsewhere: output switches to a decimal string past 15 digits, and each successful call costs $0.001 USDC via x402 on Solana with an HTTPS fallback endpoint. Those are exactly the payment and return-type facts an agent needs before invoking.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loads the purpose, then the example, then constraints, then output format, then payment/transport details. Dense with no filler, though the pricing and HTTPS lines sit slightly apart from the mathematical core.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With only two integer params, no output schema, and adequate annotations, the description supplies what is missing: inclusive-range semantics, a verification example, large-value return type, and access/cost details. An agent has everything required to call it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

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 establishes that lo and hi are inclusive index bounds ('lo must not pass hi'), that both are limited to 0..200, and the worked example C(0)..C(5)=351 disambiguates inclusivity. It does not spell out what happens when lo equals hi versus a wide range, but the essentials are covered.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific computation: the sum of central binomial coefficients over the inclusive index range lo..hi, which is distinct from the sibling central_binomial (single value). The verb+resource are unambiguous, but it never names central_binomial or central_mod as the alternatives an agent should consider.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No statement of when to choose this over the 200+ sibling numeric tools (e.g. central_binomial for one term, central_mod for modular results). The only guidance is a precondition ('lo must not pass hi'), which is a constraint rather than usage routing.

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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