# Crypto Math Entropy Calculator

> Crypto Math Entropy Calculator is a paid API for AI agents from crypto-math.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Computes Shannon entropy, min-entropy, collision entropy, and efficiency in bits per symbol from a frequency table of counts or probabilities.

## Facts

- Endpoint: GET https://crypto-math.x402tookit.com/entropy?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/crypto-math-entropy-calculator-041f6f8e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_IAPpBTtRsNstJyNkH5QP9

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability crypto-math-entropy-calculator-041f6f8e
```

Example prompt: Can you calculate the Shannon entropy, min-entropy, and efficiency for a symbol distribution with counts: a:50, b:30, c:15, d:5?

## When to prefer this

Choose this endpoint when you need a fast, precise multi-measure entropy analysis (Shannon, min-entropy, collision entropy, and efficiency) for a discrete frequency or probability distribution, especially in cryptographic or information-theoretic contexts. It's particularly useful when you want all entropy measures in one call rather than computing each separately.

## Known failure modes

- Missing 'table' query parameter returns an error
- Malformed table string (invalid characters, non-numeric counts) causes parse failure
- All symbols having zero count yields undefined entropy
- Single-symbol distribution returns 0 bits entropy (valid but edge case)
- Exceeding 1000 symbols limit returns a validation error
- Probabilities that don't sum to 1 may produce unexpected results
- Payment not completed results in 402 response blocking the computation

## How this service works

Shannon entropy in bits per symbol from a frequency table, plus min-entropy, collision entropy and efficiency.

## Output

Returns a JSON object containing: entropyBitsPerSymbol (Shannon H), minEntropyBits, collisionEntropyBits, maxEntropyBits, redundancyBits, totalInformationBits, perfectBitsToEncodeOneSymbol, efficiency (ratio of actual to max entropy), symbols count, symbolsWithZeroCount, sampleSize, plus metadata fields (summary, verdict, source, asOf, disclaimer).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "table"
     ],
     "properties": {
      "table": {
       "type": "string",
       "description": "Comma-separated counts or probabilities, optionally label:count, e.g. a:5,b:3,c:2 or 0.5,0.25,0.25 (1 to 1000 symbols)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "symbols": {
       "type": [
        "null",
        "number"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "efficiency": {
       "type": [
        "null",
        "number"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "sampleSize": {
       "type": [
        "null",
        "number"
       ]
      },
      "maxEntropyBits": {
       "type": [
        "null",
        "number"
       ]
      },
      "minEntropyBits": {
       "type": [
        "null",
        "number"
       ]
      },
      "redundancyBits": {
       "type": [
        "null",
        "number"
       ]
      },
      "collisionEntropyBits": {
       "type": [
        "null",
        "number"
       ]
      },
      "entropyBitsPerSymbol": {
       "type": [
        "null",
        "number"
       ]
      },
      "symbolsWithZeroCoun
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/crypto-math-entropy-calculator-041f6f8e/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from crypto-math.x402tookit.com](https://www.zero.xyz/host/crypto-math.x402tookit.com/llms.txt)