Evidence row 3027

What was observed

{
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      "x402",
      "https://numtheory.openverbs.com/v1/factorize"
    ],
    [
      "x402",
      "https://numtheory.openverbs.com/v1/gcd"
    ],
    [
      "x402",
      "https://numtheory.openverbs.com/v1/is-prime"
    ],
    [
      "x402",
      "https://numtheory.openverbs.com/v1/lcm"
    ],
    [
      "x402",
      "https://numtheory.openverbs.com/v1/modpow"
    ],
    [
      "x402",
      "https://numtheory.openverbs.com/v1/totient"
    ]
  ],
  "name": "numtheory.openverbs.com",
  "owner_address": null,
  "raw": {
    "caip2_networks": [
      "eip155:8453"
    ],
    "category": "",
    "description": "",
    "domain": "numtheory.openverbs.com",
    "endpoints": [
      {
        "description": "Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime.",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
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            "example": "42",
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        ],
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        },
        "providerName": "",
        "quality": {
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        },
        "serviceName": "Prime factorization",
        "tags": [
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          "factor integer",
          "integer factors api",
          "prime factors lookup",
          "divisor count"
        ],
        "url": "https://numtheory.openverbs.com/v1/factorize"
      },
      {
        "description": "Greatest common divisor of two or more non-negative integers (arbitrary precision).",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": [],
            "group": "body",
            "name": "values",
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            "type": "array"
          }
        ],
        "pricing": {
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        },
        "providerName": "",
        "quality": {
          "l30DaysTotalCalls": "2",
          "l30DaysUniquePayers": "2"
        },
        "serviceName": "Greatest common divisor",
        "tags": [
          "greatest common divisor",
          "compute gcd",
          "gcd api",
          "common divisor lookup",
          "integer gcd"
        ],
        "url": "https://numtheory.openverbs.com/v1/gcd"
      },
      {
        "description": "Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer. Returns { prime }.",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": "42",
            "group": "body",
            "name": "n",
            "required": false,
            "type": "string"
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        ],
        "pricing": {
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        },
        "providerName": "",
        "quality": {
          "l30DaysTotalCalls": "1",
          "l30DaysUniquePayers": "1"
        },
        "serviceName": "Primality test",
        "tags": [
          "primality test",
          "check prime number",
          "is prime api",
          "miller rabin test",
          "validate prime"
        ],
        "url": "https://numtheory.openverbs.com/v1/is-prime"
      },
      {
        "description": "Least common multiple of two or more positive integers (arbitrary precision).",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": [],
            "group": "body",
            "name": "values",
            "required": false,
            "type": "array"
          }
        ],
        "pricing": {
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          "currency": "USDC",
          "maxAmount": "",
          "minAmount": "",
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        },
        "providerName": "",
        "quality": {
          "l30DaysTotalCalls": "1",
          "l30DaysUniquePayers": "1"
        },
        "serviceName": "Least common multiple",
        "tags": [
          "least common multiple",
          "compute lcm",
          "lcm api",
          "common multiple lookup",
          "integer lcm"
        ],
        "url": "https://numtheory.openverbs.com/v1/lcm"
      },
      {
        "description": "Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": "42",
            "group": "body",
            "name": "base",
            "required": false,
            "type": "string"
          },
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": "42",
            "group": "body",
            "name": "exponent",
            "required": false,
            "type": "string"
          },
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": "42",
            "group": "body",
            "name": "modulus",
            "required": false,
            "type": "string"
          }
        ],
        "pricing": {
          "amount": "0.004",
          "currency": "USDC",
          "maxAmount": "",
          "minAmount": "",
          "network": "eip155:8453",
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        },
        "providerName": "",
        "quality": {
          "l30DaysTotalCalls": "1",
          "l30DaysUniquePayers": "1"
        },
        "serviceName": "Modular exponentiation",
        "tags": [
          "modular exponentiation",
          "mod pow",
          "compute base exponent mod",
          "fast modular power",
          "modular arithmetic api"
        ],
        "url": "https://numtheory.openverbs.com/v1/modpow"
      },
      {
        "description": "Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed from the prime factorization).",
        "method": "POST",
        "parameters": [
          {
            "default": null,
            "description": "",
            "enumValues": [],
            "example": "42",
            "group": "body",
            "name": "n",
            "required": false,
            "type": "string"
          }
        ],
        "pricing": {
          "amount": "0.004",
          "currency": "USDC",
          "maxAmount": "",
          "minAmount": "",
          "network": "eip155:8453",
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        },
        "providerName": "",
        "quality": {
          "l30DaysTotalCalls": "1",
          "l30DaysUniquePayers": "1"
        },
        "serviceName": "Euler's totient",
        "tags": [
          "euler totient",
          "compute phi",
          "totient function",
          "coprime count",
          "number theory totient"
        ],
        "url": "https://numtheory.openverbs.com/v1/totient"
      }
    ],
    "enriched": false,
    "iconUrl": "",
    "id": "numtheory-openverbs-com",
    "integrationType": "",
    "isNew": false,
    "name": "numtheory.openverbs.com",
    "networks": [
      "Base"
    ],
    "priceSummary": {
      "avgCostBasis": "exact",
      "avgCostPerTransaction": "0.004",
      "currency": "USDC",
      "maxAmount": "0.004",
      "minAmount": "0.004"
    },
    "provider": "numtheory.openverbs.com",
    "providerUrl": "",
    "serviceName": "",
    "tags": [
      "prime factorization",
      "factor integer",
      "integer factors api",
      "prime factors lookup",
      "divisor count",
      "greatest common divisor",
      "compute gcd",
      "gcd api",
      "common divisor lookup",
      "integer gcd",
      "primality test",
      "check prime number",
      "is prime api",
      "miller rabin test",
      "validate prime",
      "least common multiple",
      "compute lcm",
      "lcm api",
      "common multiple lookup",
      "integer lcm",
      "modular exponentiation",
      "mod pow",
      "compute base exponent mod",
      "fast modular power",
      "modular arithmetic api",
      "euler totient",
      "compute phi",
      "totient function",
      "coprime count",
      "number theory totient"
    ]
  },
  "source": "agentic_market",
  "summary": ""
}

What the leaf hashes

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Proof

Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of 2026-10-26 (296695 rows).

1. 0x5fedcd91355a67af083b3f1564089004701ddc8cb81f0f0702620806d37578f5
2. 0x4dca6890fe159a1348cf8c65eb7ab8087457c6ac0a127a30b6a96eb7a6c97eb0
3. 0x1910c5be548ea377817bb583007725d8f4b59c01fc50345b6c583980eded6b50
4. 0x5ea1b0b67bbdcc64d7129f6991cc57c5e6690cffe9b718756227fd89956ea8b7
5. 0x4b81b1ecbb6118a2b02237efd199c025f8b4e25a63eb5713cf91f891c3e22bae
6. 0x1d5e431e7382c290acd7b9152d5d6815547b1ce31c209bfb0770aa3235286531
7. 0xfd08abae22bbc77e1f874a8f028078b0638a2c7517f1b621f75012fdfd3653bc
8. 0x15ee35aee0027580c88f3c4831389c36b729ad29b0ac3dedf14105cdd25576ae
9. 0x315448cbf783ffee4b0f77fbd8394a707e36af281b068ca2464c2295e113096d
10. 0x360237a2ff9bba9982b36dddf68bf6bc616012537d41d3a91a43fe37caee345d
11. 0xa50fca837a4f035829bddff38d023aff0ec4482f9bb5df60ea5b321b01e3e922
12. 0xf4e3bedc99674db9d8ab4bc7655992ec76f822b327e6c89599b0baa3756fbd19
13. 0x89fcaf55e37dd777228f271b79ea895534a66ec0d184363c2a6eb1b4d23c9ef1
14. 0x216cebb9ae5414599109a02297c4817d7d1c6b1394afeb97efe38e32f0053974
15. 0x7726154b91b2ad65b13849ef6cb6443b1f0ff113a3089c9bd5f2bcfc16be099d
16. 0x47b89901b0f07938a6b9a66ddf35683903f79d756a7c7763665fd632758b08d0
17. 0x9a83be955a206deb65b995adfd92c58fa31c95fbbf926bd199d300e70b08b26d
18. 0x20704208aa6923d6b2450ef74ede87a6e0265d46447926038fe9506e9e154b2d
19. 0x9b9ce5b74b9bab5121612ef6b64920a8d453cbf311096a423eef9702747e868a

Day root

0xf43e8dcc3d451a4788b26be904c55e8c4c0fa75c9666796c51db38d37e2c0df8

Chained

0x702d5ac508f08b0d1accf36af25822d8e5660367494edd17a642fb61e158a57a

Published

On Arc Testnet, block 69251483: 0x495162f8936e19f0039918feebe6c307f327cd6bf8c37219620b1970041fa9ae