← The evidence ledger
Evidence row 567864
Observed , by probe.mcp/1.
- Kind
- mcp.tools
- About
- endpoint 627fcc15-7e91-413a-a75a-70195fae4f7b
- Recorded
- Previous row
- None: the first of its kind about this subject
- Body SHA-256
- ea85cea14fa8d457ab178a72d3a3587162d1fa04c2a5a8a0a8a306481986b104
- Leaf
- 0x12ad249adbf7b4c31ac8170b39aac8bf56b13a577df329f694513164738c8f33
What was observed
{
"count": 4,
"tools": [
{
"description": "Request a feature that Occam doesn't support yet.\n\n Use this when you need a capability that Occam doesn't currently\n offer. Requests are logged and used to prioritize development.\n\n Rate limit: 5 requests/hour per IP, 50/hour global — stricter than\n the compute tools' 10/hour to prevent log flooding. Descriptions\n longer than 500 characters are truncated.\n ",
"inputSchema": {
"properties": {
"description": {
"description": "A short description of the feature you need. Examples: 'LaTeX output for equations', 'support for ODE constraints', 'GPU-accelerated search', 'larger dataset limits'. Helps prioritize development.",
"title": "Description",
"type": "string"
}
},
"required": [
"description"
],
"title": "request_featureArguments",
"type": "object"
},
"name": "feature_request"
},
{
"description": "Evolutionary Symbolic Regression (PySR).\n\n Discovers algebraic equations y = f(x1, x2, ...) from feature/target\n data. Returns a Pareto front ranked by the complexity/accuracy\n tradeoff. Slower than SINDy (10-60s); searches often terminate early\n on convergence. For differential equations from time series, use\n sindy_run instead.\n\n Pricing: free tier up to 100 rows × 8 features, 60s timeout. Beyond\n that, $0.25 + $0.03 per 100 extra rows + $0.01 per extra feature\n squared, timeout up to 300s (5 min), via x402 (USDC on Base) or\n MPP/Stripe. MPP/Stripe adds a flat $0.35 per-transaction fee (Stripe\n processing), so the MPP challenge amount in a `payment_required`\n response is $0.35 higher than the x402 amount for the same base\n price; x402 gets the lower rate. Omit `payment` for free-tier\n requests; paid requests without a valid credential receive a\n `payment_required` result with pricing and accepted schemes. Full\n pricing: occam://pricing\n\n Advisory limits: jobs over 50,000 rows or 20 features are accepted\n but may not converge; response carries a top-level `warning`.\n\n Operators: fixed supported set only — custom operators (e.g.\n 'inv(x) = 1/x') are rejected. Unary: sin, cos, tan, exp, log, log2,\n log10, sqrt, abs, sinh, cosh, tanh. Binary: +, -, *, /, ^.\n See also prompt `supported_operators`.\n\n Loss metric: `loss` (in `pareto_front[].loss` and `best_loss`) is\n mean squared error between model prediction and `y` on the full\n training set — not RMSE, and not normalized by Var(y). A threshold\n appropriate for one dataset scales with y's magnitude, so set\n `loss_threshold` with that in mind (e.g. for y values near 1.0,\n 1e-6 is a tight fit; for y near 1000, the equivalent is 1.0).\n\n Early termination: set `loss_threshold` to stop at your noise floor.\n The server also stops when the search stalls (<1% improvement in the\n last third of the budget); disable with `stall_detection=false`.\n Response `stop_reason` is one of: loss_threshold, stall, timeout,\n natural.\n\n If `feature_names` is supplied, its length must equal the number of\n columns in `X`; a mismatch is rejected with a validation error.\n\n Follow-up: call `pysr_uncertainty` with a chosen expression and the\n same dataset for bootstrap confidence intervals on its fit constants\n and optional prediction bands.\n\n Rate limit: 10 requests/hour per IP, 200/hour global, max queue\n depth 20 (shared with sindy_run and pysr_uncertainty).\n\n Response (success) includes `pareto_front[]` (each with `complexity`,\n `loss`, `expression`, `expression_latex`), `best_expression`,\n `best_expression_latex`, `best_loss`, `best_complexity`, `stop_reason`,\n `elapsed_seconds`, `queue_seconds` (>0 = server saturated; use as\n backoff signal), optional `warning`, optional `_meta` (MPP receipt).\n Full response and payment-required schemas: occam://tool-schemas\n\n Example request:\n X=[[0.0], [1.0], [2.0], [3.0], [4.0]], y=[1.0, 3.0, 5.0, 7.0, 9.0],\n feature_names=[\"x\"], max_complexity=10, timeout_seconds=15\n\n Policy: occam://privacy-policy — Citation: occam://citation-info\n ",
"inputSchema": {
"properties": {
"X": {
"description": "2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features.",
"examples": [
[
[
0
],
[
1
],
[
2
],
[
3
],
[
4
]
]
],
"items": {
"items": {
"type": "number"
},
"type": "array"
},
"minItems": 5,
"title": "X",
"type": "array"
},
"binary_operators": {
"anyOf": [
{
"items": {
"type": "string"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Allowed binary operators, drawn from the fixed supported set: +, -, *, /, ^. Custom operators are NOT supported. Default: +, -, *, /. Pass [] for none.",
"title": "Binary Operators"
},
"feature_names": {
"anyOf": [
{
"items": {
"type": "string"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Names for each variable/feature column. Defaults to x0, x1, ...",
"title": "Feature Names"
},
"loss_threshold": {
"anyOf": [
{
"exclusiveMinimum": 0,
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Optional early-stop threshold on the best loss found. If set, the search terminates as soon as any Pareto-front member reaches a loss at or below this value, even if the timeout has not been reached. Useful when you know your noise floor. Default: None (no user threshold; the search runs until the stall detector or timeout).",
"title": "Loss Threshold"
},
"max_complexity": {
"default": 20,
"description": "Maximum expression tree size. Higher allows more complex expressions. Default 20, max 25.",
"maximum": 25,
"minimum": 1,
"title": "Max Complexity",
"type": "integer"
},
"payment": {
"anyOf": [
{
"additionalProperties": true,
"type": "object"
},
{
"type": "string"
},
{
"type": "null"
}
],
"default": null,
"description": "Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}. For prepaid API key: {\"scheme\":\"prepaid\",\"api_key\":\"occ_live_...\",\"request_id\":\"<optional uuid>\"}.",
"title": "Payment"
},
"populations": {
"default": 15,
"description": "Number of evolutionary populations for the search. Default 15, max 20.",
"maximum": 20,
"minimum": 1,
"title": "Populations",
"type": "integer"
},
"stall_detection": {
"default": true,
"description": "When true (default), the server stops the search early if the best loss has not improved by more than 1% during the last third of the time budget. This reclaims compute once the search has converged. Set to false only if you want the search to run for the full timeout regardless of progress.",
"title": "Stall Detection",
"type": "boolean"
},
"timeout_seconds": {
"default": 60,
"description": "Wall clock time limit in seconds. Free tier: max 60. Paid tier: max 300 (5 minutes). Default 60.",
"maximum": 300,
"minimum": 1,
"title": "Timeout Seconds",
"type": "integer"
},
"unary_operators": {
"anyOf": [
{
"items": {
"type": "string"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Allowed unary operators, drawn from the fixed supported set: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Custom operators (e.g. 'inv(x) = 1/x') are NOT supported — only the names listed are accepted. Default: sin, cos, exp, log, sqrt. Pass [] for none.",
"title": "Unary Operators"
},
"y": {
"description": "Target values, one per row of X.",
"examples": [
[
1.02,
2.97,
5.01,
7.03,
8.98
]
],
"items": {
"type": "number"
},
"minItems": 5,
"title": "Y",
"type": "array"
}
},
"required": [
"X",
"y"
],
"title": "run_pysr_toolArguments",
"type": "object"
},
"name": "pysr_run"
},
{
"description": "Bootstrap confidence intervals for the numeric constants of a\n frozen expression, plus optional prediction bands on an x-grid.\n\n Typical flow: call pysr_run, pick an expression from the response\n (best_expression or a pareto_front entry), pass it back here with\n the same dataset to get CIs on its fit constants.\n\n Returns frequentist bootstrap confidence intervals, not Bayesian\n credible intervals — posterior inference over expression structures\n is an open research problem. This tool freezes the expression\n chosen by the caller and bootstraps only its numeric constants;\n uncertainty about *which* expression is correct is not quantified.\n\n Bootstrap semantics:\n - If y_sigma is supplied, uses parametric bootstrap\n (y_b = y + Normal(0, y_sigma)). CI reflects user-stated\n measurement noise.\n - Otherwise uses residual bootstrap: fit once, resample residuals.\n CI reflects estimated-from-residuals noise.\n\n Only Float constants in the expression become free parameters.\n Integers stay structural (the 2 in x**2 is a function-class choice,\n not a fit constant). Expressions with no Float constants\n (e.g. \"x + y\") will be rejected with a validation error.\n\n Expression grammar: the `expression` string is parsed by sympy.\n Accepted operators are the same set pysr_run emits: unary `sin`,\n `cos`, `tan`, `exp`, `log`, `log2`, `log10`, `sqrt`, `abs`, `sinh`,\n `cosh`, `tanh`; binary `+`, `-`, `*`, `/`, `^` (or `**`). Whitespace\n and parenthesization are free. Every free symbol in the expression\n must correspond to an entry in `feature_names` — an unrecognised\n symbol is silently treated as a fresh sympy Symbol and the fit will\n fail downstream rather than reject early. Parse failures (syntax\n errors, malformed operators) surface as tool errors.\n\n If `feature_names` is supplied, its length must equal the number of\n columns in `X`; a mismatch is rejected with a validation error.\n\n Pricing: always free, regardless of dataset size. This tool has no\n `payment` parameter and is never subject to the x402/Stripe gate.\n Large bootstrap jobs still count against the shared rate limit\n below, so budget `n_resamples` accordingly.\n\n Rate limit: 10 requests/hour per IP, 200/hour global, max queue\n depth 20 (shared with sindy_run and pysr_run).\n ",
"inputSchema": {
"properties": {
"X": {
"description": "2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features.",
"examples": [
[
[
0
],
[
1
],
[
2
],
[
3
],
[
4
]
]
],
"items": {
"items": {
"type": "number"
},
"type": "array"
},
"minItems": 5,
"title": "X",
"type": "array"
},
"alpha": {
"default": 0.05,
"description": "Significance level. 0.05 → 95%% CI. Default 0.05.",
"exclusiveMaximum": 1,
"exclusiveMinimum": 0,
"title": "Alpha",
"type": "number"
},
"expression": {
"description": "The expression to bootstrap, as returned by pysr_run (`best_expression` or a `pareto_front[i].expression`). Only numeric Float constants are treated as free parameters — integers in the expression (e.g. the 2 in x**2) stay structural.",
"examples": [
"2.0*x0 + 1.0"
],
"title": "Expression",
"type": "string"
},
"feature_names": {
"anyOf": [
{
"items": {
"type": "string"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Names for each variable/feature column. Defaults to x0, x1, ...",
"title": "Feature Names"
},
"n_resamples": {
"default": 100,
"description": "Number of bootstrap resamples. Higher = tighter CIs, more compute. Default 100.",
"maximum": 500,
"minimum": 10,
"title": "N Resamples",
"type": "integer"
},
"x_grid": {
"anyOf": [
{
"items": {
"items": {
"type": "number"
},
"type": "array"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Optional 2D grid of feature values at which to report a prediction band. Must have the same number of columns as X. Omit to skip prediction-band computation.",
"title": "X Grid"
},
"y": {
"description": "Target values, one per row of X.",
"examples": [
[
1.02,
2.97,
5.01,
7.03,
8.98
]
],
"items": {
"type": "number"
},
"minItems": 5,
"title": "Y",
"type": "array"
},
"y_sigma": {
"anyOf": [
{
"items": {
"type": "number"
},
"type": "array"
},
{
"type": "number"
},
{
"type": "null"
}
],
"default": null,
"description": "Optional per-point measurement standard deviations, or a single scalar applied to all points. When supplied, the helper uses parametric bootstrap (y_b = y + Normal(0, y_sigma)); otherwise it uses residual bootstrap. Supplying y_sigma also improves the initial weighted fit.",
"title": "Y Sigma"
}
},
"required": [
"expression",
"X",
"y"
],
"title": "run_pysr_uncertainty_toolArguments",
"type": "object"
},
"name": "pysr_uncertainty"
},
{
"description": "Sparse Identification of Nonlinear Dynamics (SINDy).\n\n Recovers governing differential equations (dx/dt = f(x)) from time\n series data. Returns human-readable sparse expressions. Fast (seconds).\n For algebraic y = f(x) relationships without time structure, use\n pysr_run instead.\n\n Pricing: free tier up to 100 rows and 8 variables. Beyond that,\n $0.05 + $0.01 per 100 extra rows + $0.01 per extra variable squared,\n via x402 (USDC on Base) or MPP/Stripe. MPP/Stripe adds a flat $0.35\n per-transaction fee (Stripe processing), so the MPP challenge amount\n in a `payment_required` response is $0.35 higher than the x402 amount\n for the same base price; x402 gets the lower rate. Omit `payment`\n for free-tier requests; paid requests without a valid credential\n receive a `payment_required` result with pricing and accepted schemes.\n Full pricing table as structured JSON: occam://pricing\n\n Advisory limits: jobs over 500,000 rows or 50 variables are accepted\n but may not converge within the time budget; the response carries a\n top-level `warning` the agent should surface and treat as tentative.\n\n If `feature_names` is supplied, its length must equal the number of\n data columns; a mismatch is rejected with a validation error.\n\n Rate limit: 10 requests/hour per IP, 200/hour global, max queue\n depth 20 (shared with pysr_run and pysr_uncertainty).\n\n Response (success) includes `equations[]` (each with `variable`,\n `equation`, `expression`, `expression_latex`, `r2`), `library_terms`,\n `nonzero_terms`, `elapsed_seconds`, `canonical_match` (dict with\n `system`, `form`, `variable_map`, `parameter_map`, `confidence` if\n the discovered system matches one of Lorenz / Lotka-Volterra /\n Van der Pol / Duffing; `null` otherwise), optional `warning`,\n optional `_meta` (MPP receipt on paid calls). Full response and\n payment-required schemas: occam://tool-schemas\n\n Example request:\n data=[[1.0, 0.0], [0.95, -0.31], [0.81, -0.59]], t=[0.0, 0.1, 0.2],\n feature_names=[\"x\", \"y\"], poly_degree=2, threshold=0.1\n\n Policy: occam://privacy-policy — Citation: occam://citation-info\n ",
"inputSchema": {
"properties": {
"data": {
"description": "2D array of time series data. Each row is a timestep, each column is a state variable. Minimum 3 rows (finite-difference derivative). Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables.",
"examples": [
[
[
1,
0
],
[
0.9553,
-0.2955
],
[
0.8253,
-0.5646
],
[
0.6216,
-0.7833
],
[
0.3624,
-0.932
],
[
0.0707,
-0.9975
],
[
-0.2272,
-0.9738
],
[
-0.5048,
-0.8632
],
[
-0.7374,
-0.6755
],
[
-0.9041,
-0.4274
],
[
-0.99,
-0.1411
],
[
-0.9875,
0.1577
]
]
],
"items": {
"items": {
"type": "number"
},
"type": "array"
},
"minItems": 3,
"title": "Data",
"type": "array"
},
"feature_names": {
"anyOf": [
{
"items": {
"type": "string"
},
"type": "array"
},
{
"type": "null"
}
],
"default": null,
"description": "Names for each variable/feature column. Defaults to x0, x1, ...",
"title": "Feature Names"
},
"max_iter": {
"default": 20,
"description": "Maximum STLSQ optimizer iterations. Default 20.",
"maximum": 100,
"minimum": 1,
"title": "Max Iter",
"type": "integer"
},
"payment": {
"anyOf": [
{
"additionalProperties": true,
"type": "object"
},
{
"type": "string"
},
{
"type": "null"
}
],
"default": null,
"description": "Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}. For prepaid API key: {\"scheme\":\"prepaid\",\"api_key\":\"occ_live_...\",\"request_id\":\"<optional uuid>\"}.",
"title": "Payment"
},
"poly_degree": {
"default": 2,
"description": "Polynomial library degree for SINDy candidate functions. Default 2.",
"maximum": 5,
"minimum": 1,
"title": "Poly Degree",
"type": "integer"
},
"t": {
"description": "Timestamps corresponding to each row of data. Length must match row count.",
"examples": [
[
0,
0.3,
0.6,
0.9,
1.2,
1.5,
1.8,
2.1,
2.4,
2.7,
3,
3.3
]
],
"items": {
"type": "number"
},
"minItems": 3,
"title": "T",
"type": "array"
},
"threshold": {
"default": 0.1,
"description": "STLSQ sparsity threshold. Higher values produce sparser equations. Default 0.1.",
"exclusiveMinimum": 0,
"title": "Threshold",
"type": "number"
}
},
"required": [
"data",
"t"
],
"title": "run_sindy_toolArguments",
"type": "object"
},
"name": "sindy_run"
}
]
}What the leaf hashes
{"body":"ea85cea14fa8d457ab178a72d3a3587162d1fa04c2a5a8a0a8a306481986b104","id":567864,"kind":"mcp.tools","method":"probe.mcp/1","observed_us":1793138854311892,"prev":null,"subject":"627fcc15-7e91-413a-a75a-70195fae4f7b","subject_kind":"endpoint"}Proof
Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of (273461 rows).
- 0x12ad2ff0c9b28eddc716b66860ce911825eec5bc6aebeaad0de864a209f36e37
- 0xb0fdf26bc7d79d419fb6f57c3ce72f8e1895952c05da1d5cce21f1204ec1dd93
- 0xe58bfd03800fa17625715d4d2cd9a2d482bdb459154246be906b43fd0d99c1f1
- 0xc6d10cbb7928bdb7fa0703867b17f197f805e3ced97dc529140b0ec122228569
- 0x642e72aa10632a2de325ba3fe0712d44277110c77b557cd347c0635801b79509
- 0x833f819ed3f7f90a37b1a4b9dab581f327d401cc0be68da025735b8f78a99843
- 0x081e1f4951d6e73e39dd989771f7ac7c39b4c061db5fbf751eb11c9c7ace3596
- 0x921711efe29e92dc723b082cb6bc9038e8df7f285f7cc5e0b380e9c8fe5c7795
- 0x193d4ca77fd18f5603eed9950af686b4fc90040aaa394672f65d04155765608d
- 0xa09ed7b0630e96460b870ee10d5404bc0c7fafc2746919271d1675bb24fd99c9
- 0xf3282d08aac8493b8388904acc143add67b80dc96ecc149d4372cab1977d5e98
- 0x7578555e40efa7fabcea1fc203440565253b358954d398ba44e9e10d228eb3b9
- 0xedf6ab3c3733ce137d888d3e5f7006ba77ab04b8f1fe576519f7b056959665ee
- 0x52c5141da0cbee106a30396ee7d1360fd22f55084aca2ca436c8007892775670
- 0x6913cb48392acb8dc5c940dcdb6e6fc889d544f85dff11da249551a5f027e688
- 0x518b93854db03dc9fc938883abf30da6eaae5ae0d4336903968fd32a7df8c71b
- 0x22c1fb9487ee0b9732fa017a0cc321eb27a60c08450d112f755089796e12cb1c
- 0xa20d48798a34aba12eb9c7297722982d910f06c148f5e27ac59307422964a585
- 0x9fc354c0ea3efc3f1b6548bb77ea902a50f2c9647647ea61592efce2bd795699
- Day root
- 0xdd77e5e99da32c3f154180d63e3c3e6fe11e896a2c6896412ef6b5c4bcf7e795
- Chained
- 0x23bb4dfd09f55c15ac3962f53578e02c6114d5bfd9bb451cf8794fb6e2817ef4
- Published
- On Arc Testnet, block 69414147: 0xb2ebd83aafeb765a0ce66e76aefb133ed06606c98038fd56191e2bcd1dcb77b4