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Hofstadter Sum

hofstadter_sum
Read-onlyIdempotent

The sum of Hofstadter G from 0 through n. Through 0 it is 0, through 1 it is 1, through 5 it is 10, and through 10 it is 35. n runs from 0 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/hofstadter-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": {
      "n": "<n>"
    },
    "name": "hofstadter_sum"
  }
}

Input Schema

NameRequiredDescriptionDefault
nYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A3.7/5.0
Behavior4/5

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

Annotations already declare read-only, idempotent, open-world, non-destructive behavior. The description adds useful operational context: $0.001 USDC per successful call via x402 on Solana and an equivalent HTTPS endpoint. It does not describe error behavior, but the key behavioral traits are disclosed.

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-loads the core definition, then compactly supplies examples, valid range, price, and HTTPS endpoint. Every sentence contributes useful information without padding.

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 simple one-parameter arithmetic tool with no output schema, the description supplies enough to call it correctly: domain, range, example outputs, and payment model. It could be stronger with explicit sibling routing, but the core contract is complete.

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?

With 0% schema description coverage, the description compensates by defining n as an inclusive upper bound and giving concrete outputs for n=0, 1, 5, and 10. The schema already states min/max, so the added interpretation and examples are meaningful.

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 operation and scope: the cumulative sum of Hofstadter G from 0 through n. This distinguishes it from a single-term tool like hof_g, though it does not explicitly name alternatives among the many hof* siblings.

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?

Gives the valid n range and pricing, but provides no explicit when-to-use guidance, prerequisites, or comparison against sibling tools such as hof_g or hof_q_sum. The agent must infer that this is for cumulative sums rather than individual terms.

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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