Evidence row 2201583

What was observed

{
  "endpoints": [
    [
      "x402",
      "https://math-stats.x402tookit.com/combinatorics"
    ]
  ],
  "name": "Math and Statistics",
  "owner_address": "0xb531320805c5bed1d46aeadcf4f008fdf172dbda",
  "raw": {
    "accepts": [
      {
        "amount": "20000",
        "asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
        "extra": {
          "name": "USD Coin",
          "version": "2"
        },
        "maxTimeoutSeconds": 300,
        "network": "eip155:8453",
        "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
        "scheme": "exact"
      },
      {
        "amount": "20000",
        "asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
        "extra": {
          "feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM",
          "transactionVersions": [
            0
          ]
        },
        "maxTimeoutSeconds": 300,
        "network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
        "payTo": "DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s",
        "scheme": "exact"
      },
      {
        "amount": "20000",
        "asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
        "extra": {
          "name": "USD Coin",
          "version": "2"
        },
        "maxTimeoutSeconds": 300,
        "network": "eip155:137",
        "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
        "scheme": "exact"
      },
      {
        "amount": "20000",
        "asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
        "extra": {
          "name": "USD Coin",
          "version": "2"
        },
        "maxTimeoutSeconds": 300,
        "network": "eip155:42161",
        "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
        "scheme": "exact"
      }
    ],
    "description": "Exact counts: factorial, combinations, permutations, with repetition, derangements and Catalan numbers, as big integers.",
    "extensions": {
      "bazaar": {
        "info": {
          "input": {
            "method": "GET",
            "queryParams": {
              "k": 5,
              "n": 52
            },
            "type": "http"
          },
          "output": {
            "example": {
              "asOf": "2026-10-11T06:26:05.813Z",
              "catalan": "29869166945772625950142417512",
              "combinations": "2598960",
              "combinationsWithRepetition": "3819816",
              "degraded": false,
              "derangements": "29672484407795138298279444403649511427278111361911893663894333196201",
              "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
              "factorial": "80658175170943878571660636856403766975289505440883277824000000000000",
              "factorialDigits": 68,
              "factorialScientific": "8.06581e+67",
              "k": "5",
              "n": "52",
              "notChecked": [
                "problems that need the inclusion-exclusion or Stirling-number setups beyond these standard counts",
                "results are exact; very large values are also given in scientific notation (approximate)"
              ],
              "permutations": "311875200",
              "permutationsWithRepetition": "380204032",
              "reasons": [
                "Exact big-integer arithmetic. Derangements: permutations with no fixed point. Catalan(n) = C(2n,n)/(n+1).",
                "Order matters for permutations, not for combinations."
              ],
              "source": "computed locally",
              "summary": "C(52,5) = 2598960; P(52,5) = 311875200.",
              "verdict": "COUNTED"
            },
            "type": "json"
          }
        },
        "schema": {
          "$schema": "https://json-schema.org/draft/2020-12/schema",
          "properties": {
            "input": {
              "additionalProperties": false,
              "properties": {
                "method": {
                  "enum": [
                    "GET"
                  ],
                  "type": "string"
                },
                "queryParams": {
                  "properties": {
                    "k": {
                      "description": "k for combinations and permutations (0 to n, or any k for repetition)",
                      "type": "integer"
                    },
                    "n": {
                      "description": "n, 0 to 2000",
                      "type": "integer"
                    }
                  },
                  "required": [
                    "n"
                  ],
                  "type": "object"
                },
                "type": {
                  "const": "http",
                  "type": "string"
                }
              },
              "required": [
                "type",
                "method"
              ],
              "type": "object"
            },
            "output": {
              "properties": {
                "example": {
                  "properties": {
                    "asOf": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "catalan": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "combinations": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "combinationsWithRepetition": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "degraded": {
                      "type": [
                        "boolean",
                        "null"
                      ]
                    },
                    "derangements": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "disclaimer": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "factorial": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "factorialDigits": {
                      "type": [
                        "null",
                        "number"
                      ]
                    },
                    "factorialScientific": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "k": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "n": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "notChecked": {
                      "items": {
                        "type": "string"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "permutations": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "permutationsWithRepetition": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "reasons": {
                      "items": {
                        "type": "string"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "source": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "summary": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "verdict": {
                      "type": [
                        "null",
                        "string"
                      ]
                    }
                  },
                  "type": "object"
                },
                "type": {
                  "type": "string"
                }
              },
              "required": [
                "type"
              ],
              "type": "object"
            }
          },
          "required": [
            "input"
          ],
          "type": "object"
        }
      }
    },
    "lastUpdated": "2026-11-01T23:37:50.887Z",
    "quality": {
      "l30DaysTotalCalls": 2,
      "l30DaysUniquePayers": 2,
      "lastCalledAt": "2026-11-01T23:37:50.612Z"
    },
    "resource": "https://math-stats.x402tookit.com/combinatorics",
    "serviceName": "Math and Statistics",
    "tags": [
      "combinatorics",
      "factorial",
      "permutations",
      "combinations"
    ],
    "type": "http",
    "x402Version": 2
  },
  "source": "x402_bazaar",
  "summary": "Exact counts: factorial, combinations, permutations, with repetition, derangements and Catalan numbers, as big integers."
}

What the leaf hashes

{"body":"d49ca1fa8a0c75bf9ba9dd4c55815d63961c8589b1d1fdd4bd4db611befb42fe","id":2201583,"kind":"listing","method":"sync.x402_bazaar/1","observed_us":1793646806774962,"prev":null,"subject":"x402_bazaar:https://math-stats.x402tookit.com/combinatorics","subject_kind":"source_record"}

Proof

Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of 2026-11-02 (444186 rows).

1. 0xee8af612b9aa93d6dbcaeea38764bd7c82de6352992898972946038b78c9926f
2. 0x1069dc67c866c1005b2ccf00cf76f2d181b1d73b1f27187c40225c8c21c3deb0
3. 0x4b9545b999b37b235d79ba556db08f478b7e27d1a4391a520d0f805a531d7082
4. 0x1afc2205b9acb520d71f23fbe713c06d1abd0767626606f9531653ab968a72d6
5. 0x43777d257940ba8ba3c6e2595f0e6ea9a13c26f16870bd4bd1a90baeeee02c04
6. 0x7310eee78eef03e5ad576d7bbc7c783be0a5ebeaa93dd9c18905c6b7601d7c58
7. 0xd7bc978e1de1459592b9d3e36fc91c890fa5cdf2e2194744d8c444cdc3af7528
8. 0x3302151762245cd79bf33965fa7407aa1024efa1268936a91cd32428bc9fb615
9. 0x85a9064ee46f6bb0a0fb491dfd425564275f12fee9c7cd23463890737800ca82
10. 0x289d10558b458eda3cc9917551191f15d289cb49c8cb0be546d2d23d012e6782
11. 0x151bd83170434ccd04f82906ef73350feadc28309b6f1874e3bc7fe465fe848f
12. 0x244e5498c1a18cb79272c8888907c216b04d0ef4381a107b2d329eb22383048b
13. 0x6a66db154e32d45aa1f1ce72719d9372fd5cdf4add16d249006bd3cdb0f7c074
14. 0xbb465466dac90179fd91fd4d3b6985e80736d1ab4662dc57a78b5e5098d6f074
15. 0xde6a8fd6590b70565baa6078cbc8add8d94950fe959ebaf8c3716adcdbd78aa8
16. 0x6dd7e4db65395e8670c7c2747d44fec79e03305934ef4746bf5dbca04ec6ec49
17. 0xec5d643575d83c9e07e65deeef71943b53cbf3007e7e2b9a6ef414081509b0cc
18. 0x252cce55f1a3d5391c16f82d7f62494429a5f69b03486d4cfcfb7b2c96d6c884

Day root

0x78fecaabbe319e56f5c4b80fc02e2052e198ad24781da8832a475ff65f2002d1

Chained

0xdc35957db5d1371ca382b9152878ffece28ec7c5cb4f98fd71ddb367f8b999b2

Published

On Arc Testnet, block 70432815: 0x56b814612eb2e3e544153df3e91e1f7199106d1e430c7d8c6b653feeb9ebe9af