ScorpTech x402 API

Chebyshev Disc

chebyshev_disc

Read-onlyIdempotent

The Chebyshev discriminant identity T(n,x)^2 - (x^2-1)*U(n-1,x)^2 = 1. gap is that difference. n runs from 1 to 64. Past 15 digits t or u 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/chebyshev-disc

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": {
      "n": "<n>",
      "x": "<x>"
    },
    "name": "chebyshev_disc"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`x`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

C2.8/5.0

Behavior3/5

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

The annotations already cover read-only, idempotent, non-destructive, and open-world behavior. The description adds useful commercial/auth context (price, x402/Solana, HTTPS endpoint) and a precision note, but the 't or u' sentence is cryptic and the return shape is not described.

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?

The description is short and front-loads the identity, with no long preamble. Some fragments are cryptic and the pricing/endpoint lines are terse, but there is little wasted text.

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

Completeness2/5

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

With no output schema and 0% parameter-description coverage, the definition should be more explicit about the returned value and what 'gap' means relative to the identity. It gives the formula, n bounds, and a precision note, but an agent still cannot confidently predict the response shape.

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

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The formula does establish n as the polynomial degree and x as the evaluation point, which adds meaning beyond the bare schema. However, schema description coverage is 0%, the prose repeats only n's range, and x's role and constraints are left implicit, so compensation is only partial.

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

Purpose3/5

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

The description names the Chebyshev discriminant identity and says the output is 'that difference,' but never states the operation with a clear verb such as computes or returns. The formula gives a specific mathematical target, but it does not explicitly separate this tool from chebyshev_t, chebyshev_u, chebyshev_prod, or chebyshev_rec.

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?

There is no when-to-use or when-not guidance, no prerequisites, and no mention of the sibling Chebyshev tools. It supplies constraints and pricing, but leaves selection against alternatives entirely to the agent.

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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