ScorpTech x402 API

Apery Term

apery_term

Read-onlyIdempotent

One summand of the Apery number, C(n,k)^2 * C(n+k,k)^2. The k=1 summand of A(2) is 36 and the k=0 summand is 1. A k past n is 0. n and k run from 0 to 11. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery-term

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>",
      "k": "<k>"
    },
    "name": "apery_term"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	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, openWorld and non-destructive, so the safety profile is covered. The description adds genuinely new behavioral context: per-call cost ('$0.001 USDC per successful call (x402, Solana)') and an equivalent HTTPS endpoint, which matters for an agent choosing how to invoke it.

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?

Front-loaded with the formula, then examples, boundary rule, domain, and finally payment/transport logistics. Five short sentences, each carrying information, with no filler.

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?

For a two-integer pure-math tool with no output schema, the description covers definition, edge case, range and cost. The only unstated detail is the return type/format of the term (an integer), a minor gap for a deterministic computation.

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 the semantics — and it does by defining n and k through the binomial formula, giving concrete (n,k) examples, and stating the k>n boundary returns 0. It only restates the 0..11 bounds already enforced by schema minimum/maximum, but the formula-based meaning is real added value.

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?

The description gives the exact closed form ('C(n,k)^2 * C(n+k,k)^2') plus worked values, which pins down precisely what a single term is and implicitly separates it from the summed/sibling variants (apery_sum, apery, apery_mod). An agent can tell this computes one summand, not the total.

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?

It supplies worked examples ('k=1 summand of A(2) is 36', 'k=0 summand is 1') and the out-of-range rule ('A k past n is 0') and the domain 'n and k run from 0 to 11', which strongly implies correct usage. However, it never names an alternative or states when to prefer apery_sum/apery over this term-level tool, so routing is left to inference.

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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