← The evidence ledger
Evidence row 120408
Observed , by baseline/1.
- Kind
- listing
- About
- source_record x402_bazaar:https://saylorinnovations.com/api/math/probability
- Recorded
- Previous row
- None: the first of its kind about this subject
- Body SHA-256
- d46cf4b039e65502a9556a134df220206c86dd23ad688fda6eca1b67532bd162
- Leaf
- 0x5385a120826d16af4b94bcd10e7582ea7ee2f0f13ba6c032b16293d280d5a827
What was observed
{
"endpoints": [
[
"x402",
"https://saylorinnovations.com/api/math/probability"
]
],
"name": "Saylor Innovations Data Desk",
"owner_address": "0xa2a8df0f7caabea4e120a2568118f141569fc8aa",
"raw": {
"accepts": [
{
"amount": "10000",
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:probability-dist",
"name": "USD Coin",
"note": "Base settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:8453",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:probability-dist",
"name": "USD Coin",
"note": "Polygon settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:137",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:probability-dist",
"name": "USD Coin",
"note": "Arbitrum settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:42161",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"extra": {
"feePayer": "GVJJ7rdGiXr5xaYbRwRbjfaJL7fmwRygFi1H6aGqDveb",
"memo": "saylor:datadesk:probability-dist",
"reference": "8QGYJZ8NK8W7hyvkidXySrCQ3arAGjMSCNbiBeo2V6eF",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpwcm9iYWJpbGl0eS1kaXN0cmlidXRpb25zIiwicmVmZXJlbmNlIjoiOFFHWUpaOE5LOFc3aHl2a2lkWHlTckNRM2FyQUdqTVNDTmJpQmVvMlY2ZUYiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOiJFUGpGV2RkNUF1ZnFTU3FlTTJxTjF4enliYXBDOEc0d0VHR2tad3lURHQxdiIsIm1pbkFtb3VudCI6MTAwMDAsImV4cCI6MTc5MjM3Nzc2NzY1Mn0.Oa0-KL9qyHaqPm9EyRnn71oxpmm1QICBnsx4A0y2CsA"
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "Es9vMFrzaCERmJfrF4H2FYD4KCoNkY11McCe8BenwNYB",
"extra": {
"feePayer": "GVJJ7rdGiXr5xaYbRwRbjfaJL7fmwRygFi1H6aGqDveb",
"memo": "saylor:datadesk:probability-dist",
"reference": "Au76K11emfcdPVE7AVK2V1ueNHySvK1EE2rc7E3hCC3q",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpwcm9iYWJpbGl0eS1kaXN0cmlidXRpb25zIiwicmVmZXJlbmNlIjoiQXU3NksxMWVtZmNkUFZFN0FWSzJWMXVlTkh5U3ZLMUVFMnJjN0UzaENDM3EiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOiJFczl2TUZyemFDRVJtSmZyRjRIMkZZRDRLQ29Oa1kxMU1jQ2U4QmVud05ZQiIsIm1pbkFtb3VudCI6MTAwMDAsImV4cCI6MTc5MjM3Nzc2NzY1Mn0.AlBe99lMEcyIzJFzJA-XF26L2jH7T1WkmOBBNzp4y_Y"
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
},
{
"amount": "92476",
"asset": "So11111111111111111111111111111111111111112",
"extra": {
"memo": "saylor:datadesk:probability-dist",
"native": true,
"note": "Native SOL: send lamports with a system transfer, not an SPL transfer. Price is quoted live and this quote expires in 120s.",
"quotedLamports": "95337",
"reference": "8zKQcP3zKFWwTdvDHVViC69xXAPLKBZy7qex1t54eByb",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpwcm9iYWJpbGl0eS1kaXN0cmlidXRpb25zIiwicmVmZXJlbmNlIjoiOHpLUWNQM3pLRld3VGR2REhWVmlDNjl4WEFQTEtCWnk3cWV4MXQ1NGVCeWIiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOm51bGwsIm1pbkFtb3VudCI6OTI0NzYsImV4cCI6MTc5MjM3Nzc2NzY1Mn0.-dxewbrBd8n8Cljxe3w5-XZQgQqV2UqXst2OZ5dOJu0",
"solUsdPrice": 104.89
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
}
],
"description": "Binomial, Poisson and normal distribution probabilities - exact, at most, at least, ranges, z-scores and quantiles with mean and standard deviation",
"extensions": {
"bazaar": {
"info": {
"input": {
"method": "GET",
"queryParams": {
"dist": "binomial",
"k": "8",
"n": "20",
"p": "0.3"
},
"type": "http"
},
"output": {
"example": {
"distribution": "binomial",
"k": 8,
"mean": 6,
"mode": 6,
"n": 20,
"note": "Exact binomial probabilities via log-factorials (n up to 100,000).",
"p": 0.3,
"p_at_least_k": 0.2277282026,
"p_at_most_k": 0.8866685371,
"p_exactly_k": 0.1143967397,
"p_more_than_k": 0.1133314629,
"sd": 2.04939,
"source": "binomial distribution",
"variance": 4.2
},
"type": "json"
}
},
"schema": {
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"input": {
"additionalProperties": false,
"properties": {
"method": {
"enum": [
"GET"
],
"type": "string"
},
"queryParams": {
"properties": {
"dist": {
"description": "binomial, poisson or normal",
"type": "string"
},
"k": {
"description": "number of successes or events",
"type": "string"
},
"n": {
"description": "binomial trials",
"type": "string"
},
"p": {
"description": "binomial success probability (or quantile probability for normal)",
"type": "string"
}
},
"required": [
"dist",
"n",
"p",
"k"
],
"type": "object"
},
"type": {
"const": "http",
"type": "string"
}
},
"required": [
"type",
"method"
],
"type": "object"
},
"output": {
"properties": {
"example": {
"properties": {
"distribution": {
"description": "Distribution used: binomial, poisson or normal",
"type": "string"
},
"k": {
"description": "Value the probabilities refer to",
"type": [
"number",
"null"
]
},
"mean": {
"description": "Mean of the distribution",
"type": "number"
},
"mode": {
"description": "Mode used",
"type": [
"number",
"null"
]
},
"n": {
"description": "Number of trials (binomial)",
"type": [
"number",
"null"
]
},
"note": {
"description": "Caveat or context for reading the result",
"type": "string"
},
"p": {
"description": "Success probability (binomial)",
"type": [
"number",
"null"
]
},
"p_at_least_k": {
"description": "P at least k",
"type": [
"number",
"null"
]
},
"p_at_most_k": {
"description": "P at most k",
"type": [
"number",
"null"
]
},
"p_exactly_k": {
"description": "P exactly k",
"type": [
"number",
"null"
]
},
"p_more_than_k": {
"description": "P more than k",
"type": [
"number",
"null"
]
},
"sd": {
"description": "Standard deviation",
"type": [
"number",
"null"
]
},
"source": {
"description": "Data source the values come from",
"type": "string"
},
"variance": {
"description": "Variance of the distribution",
"type": [
"number",
"null"
]
}
},
"required": [
"distribution",
"mean"
],
"type": "object"
},
"type": {
"const": "json",
"type": "string"
}
},
"required": [
"type"
],
"type": "object"
}
},
"required": [
"input"
],
"type": "object"
}
}
},
"iconUrl": "https://res.cloudinary.com/bdb-prod/image/upload/c_fill,ar_1:1,w_256,h_256,f_auto,q_auto/v1791811517/bazaar-icons/bc5e2b3d111ebbef.jpg",
"lastUpdated": "2026-10-19T02:40:47.696Z",
"quality": {
"l30DaysTotalCalls": 2,
"l30DaysUniquePayers": 2,
"lastCalledAt": "2026-10-19T02:40:47.395Z"
},
"resource": "https://saylorinnovations.com/api/math/probability",
"serviceName": "Saylor Innovations Data Desk",
"tags": [
"binomial probability calculator",
"probability of at least k",
"poisson probability of k events",
"normal distribution z score",
"probability between two values"
],
"type": "http",
"x402Version": 2
},
"source": "x402_bazaar",
"summary": "Binomial, Poisson and normal distribution probabilities - exact, at most, at least, ranges, z-scores and quantiles with mean and standard deviation"
}What the leaf hashes
{"body":"d46cf4b039e65502a9556a134df220206c86dd23ad688fda6eca1b67532bd162","id":120408,"kind":"listing","method":"baseline/1","observed_us":1793025618018967,"prev":null,"subject":"x402_bazaar:https://saylorinnovations.com/api/math/probability","subject_kind":"source_record"}Proof
Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of (296695 rows).
- 0x5386523c8e9872d36e9c9621ce37d81bc347d6e9f2fc27e95dbc518f75c590a5
- 0xe8d893e1e5bb5d495d93d68d2b8dc35080cebcab9ee13fd492510d40fdde1cad
- 0xb8c2b625f756a4a072c811733cbf100cc68d3ba364a651c549995862a584d776
- 0xd31a0b38dabee45717b992a1c3d0138547dbfc6265f5508f873e8e4ae8f90b8c
- 0x66683571ca753a1c04f4974fe42639800167202b9217ab50436967e78aab94f3
- 0x7d459afab3e5a8661afbb0c9ffc5dbbde8cf9aeb7ee12354cf366074e5d93c9c
- 0xf7066418060e14b13637ba13c59ef2b30071b3e4f5d63ad48d980315a878eac4
- 0xde8371905cba93d00d642df3e9cc6a11feac66b20a37b3d98669173f7af1d40b
- 0x241e168d8909e2b4366a8934be8ca9d184535f22d531c2b2b6e7abbc767ceebf
- 0xd9bbd72a69ca0e31e79dc40e77b469d8ab4afe2636f7905d8e4bb75b111f8a4b
- 0xa1d1c99aa28ad1dadb7dae5386ee0342e06cf642d29909897d3feca675a6d839
- 0x774d66905c34a786c6d34bf1c4491dbdb08f534c9eb5f76cf3de03385d28f388
- 0xd830c52e1e8095e014510110592485afcb02b9c9a36f85653e4891a8de941246
- 0x0733993143f0230e79482cef2c38e95d98f9eafbe64a43cdc74a4545938a4167
- 0x2be1e80e065dd6b2cc75a7142be22225acd144ac975d70bf24b4f01fd76dc497
- 0x2e6a32eb32761c210560e852405e2f865f958ddbe01027894f8b9c1b3433b9f0
- 0x9a83be955a206deb65b995adfd92c58fa31c95fbbf926bd199d300e70b08b26d
- 0x20704208aa6923d6b2450ef74ede87a6e0265d46447926038fe9506e9e154b2d
- 0x9b9ce5b74b9bab5121612ef6b64920a8d453cbf311096a423eef9702747e868a
- Day root
- 0xf43e8dcc3d451a4788b26be904c55e8c4c0fa75c9666796c51db38d37e2c0df8
- Chained
- 0x702d5ac508f08b0d1accf36af25822d8e5660367494edd17a642fb61e158a57a
- Published
- On Arc Testnet, block 69251483: 0x495162f8936e19f0039918feebe6c307f327cd6bf8c37219620b1970041fa9ae