ScorpTech x402 Tools

Chebyshev U

chebyshev_u

Read-onlyIdempotent

The Chebyshev polynomial of the second kind U(n,x) at an integer x. U(0,x) is 1, U(1,x) is 2*x, and U(3,2) is 56. n runs from 0 to 64 and x from -1000 to 1000. 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/chebyshev-u

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_u"
  }
}

Input Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.2/5.0

Behavior4/5

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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, and the description still adds real behavioral context: the domain limits (n to 64, x to ±1000) that determine when a call is valid, the output-formatting rule ('past 15 digits the value is a decimal string'), and a per-call x402/Solana payment cost. It stops short of describing error behavior or the exact non-decimal return type.

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

Conciseness5/5

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

A single dense paragraph, front-loaded with the definition and examples before constraints, pricing, and the alternate endpoint. Every sentence carries new information; nothing is padding or restatement of the title.

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?

No output schema exists, so the description must speak to return values, and it partially does via the 15-digit decimal-string rule and the worked examples that imply integer output. Payment and endpoint details round out a complete picture for a two-parameter read-only math tool; only error/overflow behavior is unstated.

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 description coverage is 0%, so the description must carry the parameter burden, and it does: it defines n as the degree (0-64) and x as the integer point (-1000 to 1000), and the U(3,2)=56 example disambiguates argument order. It still omits what happens if x=0 or negative or why those bounds exist.

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

Purpose5/5

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

States a specific mathematical object and operation: 'The Chebyshev polynomial of the second kind U(n,x) at an integer x,' which is immediately distinguishable from first-kind siblings (chebyshev_t) and from chebyshev_disc/prod/rec. Concrete worked values (U(0,x)=1, U(1,x)=2*x, U(3,2)=56) remove any ambiguity about what is computed.

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

Usage Guidelines3/5

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

Gives operating bounds and a costing/payment context ('$0.001 USDC per successful call'), plus a same-tool HTTPS alternative endpoint, which is genuinely useful routing information. However, it never says when to prefer this over chebyshev_t, chebyshev_rec, or chebyshev_prod, and offers no exclusions or preconditions; usage is only implied by the domain range.

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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