Evidence row 2201234

What was observed

{
  "endpoints": [
    [
      "x402",
      "https://probability-calc.x402tookit.com/multinomial"
    ]
  ],
  "name": "Probability Calculators",
  "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": "Multinomial coefficient (arrangements of repeated items like MISSISSIPPI) and multinomial probability for given odds.",
    "extensions": {
      "bazaar": {
        "info": {
          "input": {
            "method": "GET",
            "queryParams": {
              "word": "MISSISSIPPI"
            },
            "type": "http"
          },
          "output": {
            "example": {
              "asOf": "2026-10-11T14:44:18.681Z",
              "degraded": false,
              "digits": 5,
              "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
              "formula": "11! / (1! x 4! x 4! x 2!)",
              "groupSizes": [
                1,
                4
              ],
              "letters": [
                "Mx1",
                "Ix4",
                "…2 more"
              ],
              "multinomialCoefficient": "34650",
              "notChecked": [
                "dependence between draws (the probability form assumes independent trials with fixed odds, i.e. sampling with replacement)",
                "arrangements with extra constraints such as no two equal letters adjacent"
              ],
              "reasons": [
                "Multinomial coefficient = n! / (k1! k2! ... km!): the number of distinct orderings of n items where equal items are interchangeable."
              ],
              "scientific": null,
              "source": "computed locally (exact big-integer arithmetic)",
              "summary": "11 items in groups 1, 4, 4, 2: 34650 distinct arrangements.",
              "total": 11,
              "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": {
                    "counts": {
                      "description": "Group sizes, comma separated: 1,4,4,2 (give counts or word)",
                      "type": "string"
                    },
                    "probs": {
                      "description": "Optional outcome probabilities, comma separated, one per count, summing to 1: gives the multinomial probability of exactly these counts",
                      "type": "string"
                    },
                    "word": {
                      "description": "Or a word/string: the repeated letters set the group sizes (MISSISSIPPI)",
                      "type": "string"
                    }
                  },
                  "required": [],
                  "type": "object"
                },
                "type": {
                  "const": "http",
                  "type": "string"
                }
              },
              "required": [
                "type",
                "method"
              ],
              "type": "object"
            },
            "output": {
              "properties": {
                "example": {
                  "properties": {
                    "asOf": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "degraded": {
                      "type": [
                        "boolean",
                        "null"
                      ]
                    },
                    "digits": {
                      "type": [
                        "null",
                        "number"
                      ]
                    },
                    "disclaimer": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "formula": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "groupSizes": {
                      "items": {
                        "type": "number"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "letters": {
                      "items": {
                        "type": "string"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "multinomialCoefficient": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "notChecked": {
                      "items": {
                        "type": "string"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "reasons": {
                      "items": {
                        "type": "string"
                      },
                      "type": [
                        "array",
                        "null"
                      ]
                    },
                    "scientific": {},
                    "source": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "summary": {
                      "type": [
                        "null",
                        "string"
                      ]
                    },
                    "total": {
                      "type": [
                        "null",
                        "number"
                      ]
                    },
                    "verdict": {
                      "type": [
                        "null",
                        "string"
                      ]
                    }
                  },
                  "type": "object"
                },
                "type": {
                  "type": "string"
                }
              },
              "required": [
                "type"
              ],
              "type": "object"
            }
          },
          "required": [
            "input"
          ],
          "type": "object"
        }
      }
    },
    "lastUpdated": "2026-11-02T04:07:44.153Z",
    "quality": {
      "l30DaysTotalCalls": 2,
      "l30DaysUniquePayers": 1,
      "lastCalledAt": "2026-11-02T04:07:43.975Z"
    },
    "resource": "https://probability-calc.x402tookit.com/multinomial",
    "serviceName": "Probability Calculators",
    "tags": [
      "multinomial",
      "arrangements",
      "combinatorics",
      "probability"
    ],
    "type": "http",
    "x402Version": 2
  },
  "source": "x402_bazaar",
  "summary": "Multinomial coefficient (arrangements of repeated items like MISSISSIPPI) and multinomial probability for given odds."
}

What the leaf hashes

{"body":"423f61c0b88a8457855418778d504971836874bd081601676080a3b35a07fdce","id":2201234,"kind":"listing","method":"sync.x402_bazaar/1","observed_us":1793646801680300,"prev":null,"subject":"x402_bazaar:https://probability-calc.x402tookit.com/multinomial","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. 0xfaa4a85f7973b7d7a38da02923b2a11cee4cbdf824fe90b3c7dc1f0ab03ed66d
2. 0x48b1a64e6098668a0a6744dc35a9029caacd160d28b4e2aaf5c8cd575cdd1243
3. 0x2a3a0eae1b5f2b25a0ebd9ad2bf07debced346b44dde670afb13ab44a92c0f6f
4. 0xde7ffd956c7381570a3b1b1afbd20db85b2afd8c83363cb7404598f8cdbe54f2
5. 0x5d2b921bcf00e7b12e5535c1d9d39bee034434a2bcd8c244897970a1e617f990
6. 0x7ca4ab32e5840e71e0449cb1c08902275b11da422c8cd637e761ce0a96cd7aa9
7. 0x645a3291de78d4e9ac09d95afbc7d794c653bbd1466c8acdc343844a965e27cb
8. 0xb48d4c59d0630ed222590ac8cbe7e832dfb08de0ad7783b414563457e5e60272
9. 0x806e4a92eed1919cd90004416a2dfbab7e1dbcfc2f8c95eead572a27b50376f8
10. 0xd350a98d5d904747e2af0cb080a0f675a855db6af455bb9b02373a9c02cfef8f
11. 0x8a58aa9f01814788100b857e79ca8a8885471d7ae34162bc1fa3c986741c6a39
12. 0x1fdc5cec209319ec27c935f06e49dfee099419dfa8632c827c7fdc61fcd2e0c3
13. 0x53d9a703c9e9f252a5170e08d05e1b0117ac9e5b187b8d11c1fc275324818140
14. 0x59ed3c823c7507ae1b2993d19eda543383739dde961b25c4e0927023fff6be12
15. 0x4068a4306db47ea0eae5f76e5137753caa3dbb132dca6a61a4d6c1838a52700f
16. 0x25127db2e775737b2874f6a159f7c1bf984317eea6482e94589c3ef4c5ccab32
17. 0xec5d643575d83c9e07e65deeef71943b53cbf3007e7e2b9a6ef414081509b0cc
18. 0x252cce55f1a3d5391c16f82d7f62494429a5f69b03486d4cfcfb7b2c96d6c884

Day root

0x78fecaabbe319e56f5c4b80fc02e2052e198ad24781da8832a475ff65f2002d1

Chained

0xdc35957db5d1371ca382b9152878ffece28ec7c5cb4f98fd71ddb367f8b999b2

Published

On Arc Testnet, block 70432815: 0x56b814612eb2e3e544153df3e91e1f7199106d1e430c7d8c6b653feeb9ebe9af