38 MCP tools: Rust computation, Discovery, composition, counterexample scans and signed checks.
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Compare 4–40 supplied FEN positions and played SAN/UCI moves with Stockfish: first-choice agreement and centipawn loss. Entire analysis has a 25-second deadline; no cheating verdict.
Compare 4–40 supplied FEN positions and played SAN/UCI moves with Stockfish: first-choice agreement and centipawn loss. Entire analysis has a 25-second deadline; no cheating verdict.
| Argument | Type | Description |
|---|---|---|
| depth | integer | |
| positions* | array |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"positions"
],
"properties": {
"depth": {
"type": "integer",
"default": 12,
"maximum": 20,
"minimum": 4
},
"positions": {
"type": "array",
"items": {
"type": "object",
"required": [
"fen",
"played"
],
"properties": {
"fen": {
"type": "string"
},
"played": {
"type": "string"
}
}
},
"maxItems": 40,
"minItems": 4
}
}
}Convert angular speed and candidate distances to minimum transverse speeds; check a claimed speed-distance pair. Distance hypotheses are supplied, not measured; no object-origin conclusion.
| Argument | Type | Description |
|---|---|---|
| distance_max_km | number | |
| distance_min_km | number | |
| claimed_speed_kmh | number | |
| claimed_distance_km | number | |
| angular_speed_deg_per_s* | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"angular_speed_deg_per_s"
],
"properties": {
"distance_max_km": {
"type": "number",
"default": 400000,
"maximum": 400000,
"minimum": 0.002
},
"distance_min_km": {
"type": "number",
"default": 0.01,
"maximum": 400000,
"minimum": 0.001
},
"claimed_speed_kmh": {
"type": "number",
"maximum": 500000,
"minimum": 0.1
},
"claimed_distance_km": {
"type": "number",
"maximum": 400000,
"minimum": 0.001
},
"angular_speed_deg_per_s": {
"type": "number",
"maximum": 90,
"minimum": 0.0001
}
}
}Refit original tracks plus one supplied new angular series, each counted once; compute the baseline natively. Declare synthetic/measured origin (unverified). Conditional uncertainty may worsen; forecast angles are not acquired evidence.
| Argument | Type | Description |
|---|---|---|
| objective* | object | |
| new_series* | object | |
| assumptions* | object | |
| data_origin* | string | Origin declared by the caller; even measured is not independently verified or authenticated. |
| observations* | object |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"observations",
"new_series",
"objective",
"assumptions",
"data_origin"
],
"properties": {
"objective": {
"type": "object",
"required": [
"horizon_s"
],
"properties": {
"horizon_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Absolute comparison time in the same corrected seconds as the observations; after the original observations, within their bounded 3600-second domain."
}
},
"additionalProperties": false
},
"new_series": {
"type": "object",
"required": [
"id",
"station",
"sigma_az_deg",
"sigma_el_deg",
"samples"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[A-Za-z0-9_.-]+$",
"maxLength": 64,
"minLength": 1
},
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"t_s",
"azimuth_deg",
"elevation_deg"
],
"properties": {
"t_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Already corrected absolute time; strictly after all baseline samples and no later than the comparison horizon."
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -2
}
},
"additionalProperties": false
},
"maxItems": 120,
"minItems": 3
},
"station": {
"type": "object",
"required": [
"id",
"lat",
"lon",
"elevation_m"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[A-Za-z0-9_.-]+$",
"maxLength": 64,
"minLength": 1
},
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"elevation_m": {
"type": "number",
"maximum": 9000,
"minimum": -500
}
},
"additionalProperties": false
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
}
},
"additionalProperties": false
},
"assumptions": {
"type": "object",
"required": [
"independent_new_errors",
"exact_stations_and_clocks",
"constant_velocity"
],
"properties": {
"constant_velocity": {
"type": "boolean",
"const": true
},
"independent_new_errors": {
"type": "boolean",
"const": true
},
"exact_stations_and_clocks": {
"type": "boolean",
"const": true
}
},
"additionalProperties": false
},
"data_origin": {
"enum": [
"synthetic",
"measured"
],
"type": "string",
"description": "Origin declared by the caller; even measured is not independently verified or authenticated."
},
"observations": {
"type": "object",
"required": [
"observers"
],
"properties": {
"observers": {
"type": "array",
"items": {
"type": "object",
"required": [
"lat",
"lon",
"sigma_az_deg",
"sigma_el_deg",
"samples"
],
"properties": {
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"t_s",
"azimuth_deg",
"elevation_deg"
],
"properties": {
"t_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Seconds from a common epoch, strictly increasing for this observer."
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -2
}
},
"additionalProperties": false
},
"maxItems": 120,
"minItems": 3
},
"elevation_m": {
"type": "number",
"default": 0,
"maximum": 9000,
"minimum": -500
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"clock_offset_s": {
"type": "number",
"default": 0,
"maximum": 60,
"minimum": -60,
"description": "The observer clock is ahead of the common base by this many seconds; the engine subtracts it."
}
},
"additionalProperties": false
},
"maxItems": 4,
"minItems": 2
}
},
"additionalProperties": false
}
},
"additionalProperties": false
}Apply necessary GRIM/GRIMMER checks to rounded means and sample deviations of bounded integer observations. Passing does not prove a dataset exists; inconsistency does not establish fraud.
| Argument | Type | Description |
|---|---|---|
| n* | integer | |
| sd | number | |
| mean* | number | |
| decimals | integer | |
| max_value | integer | |
| min_value | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"n",
"mean"
],
"properties": {
"n": {
"type": "integer",
"maximum": 200000,
"minimum": 2
},
"sd": {
"type": "number",
"minimum": 0
},
"mean": {
"type": "number"
},
"decimals": {
"type": "integer",
"default": 2,
"maximum": 6,
"minimum": 0
},
"max_value": {
"type": "integer",
"default": 5,
"maximum": 100,
"minimum": -100
},
"min_value": {
"type": "integer",
"default": 1,
"maximum": 100,
"minimum": -100
}
}
}Compare up to three task selections; choose highest examined value meeting the target under simultaneous 95% sampling bounds or an exact bound. Independent-uniform durations; can return inconclusive/blocked. Streams native events.
| Argument | Type | Description |
|---|---|---|
| seed | integer | |
| items* | array | |
| budget* | integer | |
| samples | integer | |
| uncertainty* | number | |
| allowed_tools | array | |
| duration_model | string | |
| max_candidates | integer | |
| min_success_rate | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"items",
"budget",
"uncertainty"
],
"properties": {
"seed": {
"type": "integer",
"default": 42,
"maximum": 4294967295,
"minimum": 0
},
"items": {
"type": "array",
"items": {
"type": "object",
"required": [
"name",
"duration",
"value"
],
"properties": {
"name": {
"type": "string",
"maxLength": 120,
"minLength": 1
},
"value": {
"type": "integer",
"maximum": 10000,
"minimum": 0
},
"duration": {
"type": "integer",
"maximum": 1440,
"minimum": 1
}
},
"additionalProperties": false
},
"maxItems": 32,
"minItems": 1
},
"budget": {
"type": "integer",
"maximum": 1440,
"minimum": 1
},
"samples": {
"type": "integer",
"default": 10000,
"maximum": 20000,
"minimum": 100
},
"uncertainty": {
"type": "number",
"maximum": 0.5,
"minimum": 0
},
"allowed_tools": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"default": [
"optimize_tasks",
"simulate_plan"
],
"maxItems": 14
},
"duration_model": {
"type": "string",
"default": "independent_uniform",
"maxLength": 64,
"minLength": 1
},
"max_candidates": {
"type": "integer",
"default": 3,
"maximum": 3,
"minimum": 1
},
"min_success_rate": {
"type": "number",
"default": 0.95,
"maximum": 0.999,
"minimum": 0.5
}
},
"additionalProperties": false
}Check an explicit arithmetic claim. Checked i128 rationals give exact verdicts when expression, claim and tolerances are representable. Unsupported functions or overflow return an estimate with an undetermined verdict. Includes a versioned integrity digest; no checks of units or model meaning.
| Argument | Type | Description |
|---|---|---|
| values | array | |
| expression* | string | |
| claimed_value* | number | |
| tolerance_absolute | number | |
| tolerance_relative | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"claimed_value",
"expression"
],
"properties": {
"values": {
"type": "array",
"items": {
"type": "object",
"required": [
"name",
"value"
],
"properties": {
"name": {
"type": "string",
"pattern": "^[A-Za-z_][A-Za-z0-9_]*$",
"maxLength": 32,
"minLength": 1
},
"value": {
"type": "number",
"maximum": 9007199254740991,
"minimum": -9007199254740991
}
},
"additionalProperties": false
},
"maxItems": 16,
"minItems": 0
},
"expression": {
"type": "string",
"maxLength": 512,
"minLength": 1
},
"claimed_value": {
"type": "number",
"maximum": 9007199254740991,
"minimum": -9007199254740991
},
"tolerance_absolute": {
"type": "number",
"maximum": 1e+300,
"minimum": 0
},
"tolerance_relative": {
"type": "number",
"maximum": 1000000000,
"minimum": 0
}
},
"additionalProperties": false
}Check a claimed Sun (soleil) or Moon (lune) position for UTC time/location using NOAA/Meeus approximations and lunar parallax. Returns model-conditional angular consistency and lunar phase.
| Argument | Type | Description |
|---|---|---|
| object | string | |
| date_utc* | string | |
| latitude* | number | |
| longitude* | number | |
| tolerance_deg | number | |
| claimed_azimuth_deg* | number | |
| claimed_elevation_deg* | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"date_utc",
"latitude",
"longitude",
"claimed_azimuth_deg",
"claimed_elevation_deg"
],
"properties": {
"object": {
"enum": [
"soleil",
"lune"
],
"type": "string",
"default": "lune"
},
"date_utc": {
"type": "string",
"maxLength": 20,
"minLength": 20
},
"latitude": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"longitude": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"tolerance_deg": {
"type": "number",
"default": 2,
"maximum": 30,
"minimum": 0.2
},
"claimed_azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"claimed_elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -90
}
}
}Compare 4–120 measured minute/azimuth pairs with solar motion: residuals, slope, direction and time-lapse speed. Supply measurements, not video. Results are model-conditional consistency findings.
| Argument | Type | Description |
|---|---|---|
| samples* | array | |
| date_utc* | string | |
| latitude* | number | |
| longitude* | number | |
| tolerance_deg | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"date_utc",
"latitude",
"longitude",
"samples"
],
"properties": {
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"minutes",
"azimuth_deg"
],
"properties": {
"minutes": {
"type": "number",
"maximum": 1440,
"minimum": 0
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
}
}
},
"maxItems": 120,
"minItems": 4
},
"date_utc": {
"type": "string",
"maxLength": 20,
"minLength": 20
},
"latitude": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"longitude": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"tolerance_deg": {
"type": "number",
"default": 5,
"maximum": 30,
"minimum": 0.5
}
}
}Plan from declared available/goal contracts within tool, locality and search bounds. Returns dependencies, blockers and existing-tool bindings. Cost counts graph steps, not speed, price or quality. Runs no engines; execution validates arguments.
| Argument | Type | Description |
|---|---|---|
| goals* | array | |
| inputs | object | |
| adapters | object | |
| available* | array | |
| constraints | object |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"goals",
"available"
],
"properties": {
"goals": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z0-9_.]+$",
"maxLength": 96,
"minLength": 1
},
"maxItems": 8,
"minItems": 1
},
"inputs": {
"type": "object",
"propertyNames": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"additionalProperties": {
"type": "object",
"propertyNames": {
"type": "string"
},
"additionalProperties": {}
}
},
"adapters": {
"type": "object",
"properties": {
"route_durations.v1": {
"type": "object",
"required": [
"speed_kmh"
],
"properties": {
"speed_kmh": {
"type": "number",
"maximum": 150,
"minimum": 1
}
},
"additionalProperties": false
}
},
"additionalProperties": false
},
"available": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z0-9_.]+$",
"maxLength": 96,
"minLength": 1
},
"maxItems": 48
},
"constraints": {
"type": "object",
"properties": {
"max_steps": {
"type": "integer",
"default": 8,
"maximum": 16,
"minimum": 1
},
"local_only": {
"type": "boolean",
"default": true
},
"allowed_tools": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"maxItems": 20
},
"max_search_states": {
"type": "integer",
"default": 512,
"maximum": 2048,
"minimum": 1
},
"max_structural_cost": {
"type": "integer",
"default": 64,
"maximum": 64,
"minimum": 1
}
},
"additionalProperties": false
}
},
"additionalProperties": false
}Compute an ideal two-body Keplerian orbit around one solar mass. Time starts at periapsis; distances use AU and time uses days. This model is not a real celestial ephemeris.
| Argument | Type | Description |
|---|---|---|
| eccentricity* | number | |
| elapsed_days* | number | |
| semi_major_au* | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"eccentricity",
"elapsed_days",
"semi_major_au"
],
"properties": {
"eccentricity": {
"type": "number",
"maximum": 0.9,
"minimum": 0
},
"elapsed_days": {
"type": "number",
"maximum": 365250,
"minimum": 0
},
"semi_major_au": {
"type": "number",
"maximum": 30,
"minimum": 0.1
}
},
"additionalProperties": false
}Run approved task-selection/route-to-duration risk chains only. Supply engine inputs and explicit uncertainty; route speed is 1–150 km/h. Returns native receipts and 95% sampling bounds. Completed means assessed, not safe. Other paths use advertised bindings.
| Argument | Type | Description |
|---|---|---|
| goals* | array | |
| inputs | object | |
| adapters | object | |
| available* | array | |
| constraints | object |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"goals",
"available"
],
"properties": {
"goals": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z0-9_.]+$",
"maxLength": 96,
"minLength": 1
},
"maxItems": 8,
"minItems": 1
},
"inputs": {
"type": "object",
"propertyNames": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"additionalProperties": {
"type": "object",
"propertyNames": {
"type": "string"
},
"additionalProperties": {}
}
},
"adapters": {
"type": "object",
"properties": {
"route_durations.v1": {
"type": "object",
"required": [
"speed_kmh"
],
"properties": {
"speed_kmh": {
"type": "number",
"maximum": 150,
"minimum": 1
}
},
"additionalProperties": false
}
},
"additionalProperties": false
},
"available": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z0-9_.]+$",
"maxLength": 96,
"minLength": 1
},
"maxItems": 48
},
"constraints": {
"type": "object",
"properties": {
"max_steps": {
"type": "integer",
"default": 8,
"maximum": 16,
"minimum": 1
},
"local_only": {
"type": "boolean",
"default": true
},
"allowed_tools": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"maxItems": 20
},
"max_search_states": {
"type": "integer",
"default": 512,
"maximum": 2048,
"minimum": 1
},
"max_structural_cost": {
"type": "integer",
"default": 64,
"maximum": 64,
"minimum": 1
}
},
"additionalProperties": false
}
},
"additionalProperties": false
}Train route-score ASTs on 1–8 supplied cases: at most 64 attempts and 31 nodes; stop between trials after 25s. Select converged candidates using training quality plus logical-fuel cost, a work proxy rather than CPU time. No held-out validation, arbitrary code or automatic promotion.
| Argument | Type | Description |
|---|---|---|
| seed* | integer | |
| train* | array | |
| budget* | object |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"train",
"seed",
"budget"
],
"properties": {
"seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0
},
"train": {
"type": "array",
"items": {
"type": "object",
"required": [
"id",
"points"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[a-zA-Z0-9_-]+$",
"maxLength": 64,
"minLength": 1
},
"points": {
"type": "array",
"items": {
"type": "object",
"required": [
"x",
"y"
],
"properties": {
"x": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"y": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
}
},
"additionalProperties": false
},
"maxItems": 32,
"minItems": 2
}
},
"additionalProperties": false
},
"maxItems": 8,
"minItems": 1
},
"budget": {
"type": "object",
"required": [
"candidates",
"fuel_per_case",
"time_per_case_ms"
],
"properties": {
"candidates": {
"type": "integer",
"maximum": 64,
"minimum": 1
},
"fuel_per_case": {
"type": "integer",
"maximum": 2000000,
"minimum": 1
},
"time_per_case_ms": {
"type": "number",
"const": 100
}
},
"additionalProperties": false
}
},
"additionalProperties": false
}Read a public contributor ticket/progress and verified pi or discrete synthetic schedule result. Schedule results include fixed-sample Wilson95 bounds. Worker/verification/wall times are separate; model probabilities are not delivery guarantees.
| Argument | Type | Description |
|---|---|---|
| job_id* | string |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"job_id"
],
"properties": {
"job_id": {
"type": "string",
"format": "uuid",
"pattern": "^([0-9a-fA-F]{8}-[0-9a-fA-F]{4}-[1-8][0-9a-fA-F]{3}-[89abAB][0-9a-fA-F]{3}-[0-9a-fA-F]{12}|00000000-0000-0000-0000-000000000000|ffffffff-ffff-ffff-ffff-ffffffffffff)$"
}
},
"additionalProperties": false
}Compute 1–12 ideal fixed/free membrane modes for a simple polygon in metres using bounded P1 finite elements. Return upper bounds, extrapolated estimates and optional frequencies/shapes. Finite spectral agreement does not prove isospectrality; no damping. CPU, direct-only; no planner binding.
| Argument | Type | Description |
|---|---|---|
| modes | integer | Default 8, counted with multiplicity. |
| polygon* | array | Vertices [x, y] in metres, either orientation; a repeated closing vertex is allowed. Must be simple. |
| boundary | any | fixed (default): drumhead, TM waveguide. free: acoustic cavity, TE waveguide. |
| wave_speed | number | m/s; √(tension/areal density) for a membrane. Enables frequency_hz and notes. |
| compare_polygon | array | Optional second shape: do the two drums sound the same? |
| include_mode_shapes | boolean | Adds a ≤1024-triangle mesh with normalized mode values, for visualization. |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"polygon"
],
"properties": {
"modes": {
"type": "integer",
"maximum": 12,
"minimum": 1,
"description": "Default 8, counted with multiplicity."
},
"polygon": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "number",
"maximum": 10000,
"minimum": -10000
},
"maxItems": 2,
"minItems": 2
},
"maxItems": 65,
"minItems": 3,
"description": "Vertices [x, y] in metres, either orientation; a repeated closing vertex is allowed. Must be simple."
},
"boundary": {
"anyOf": [
{
"type": "string",
"const": "fixed"
},
{
"type": "string",
"const": "free"
}
],
"description": "fixed (default): drumhead, TM waveguide. free: acoustic cavity, TE waveguide."
},
"wave_speed": {
"type": "number",
"maximum": 1000000000,
"minimum": 1e-9,
"description": "m/s; √(tension/areal density) for a membrane. Enables frequency_hz and notes."
},
"compare_polygon": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "number",
"maximum": 10000,
"minimum": -10000
},
"maxItems": 2,
"minItems": 2
},
"maxItems": 65,
"minItems": 3,
"description": "Optional second shape: do the two drums sound the same?"
},
"include_mode_shapes": {
"type": "boolean",
"description": "Adds a ≤1024-triangle mesh with normalized mode values, for visualization."
}
},
"additionalProperties": false
}Compare up to 32 declared deadline/optional-task changes under independent-uniform durations; preserve required tasks. Search bounds select one finalist for separately seeded confirmation, without retries. Conditional on the model, not delivery reliability.
| Argument | Type | Description |
|---|---|---|
| costs* | object | |
| items* | array | |
| samples* | integer | |
| search_seed* | integer | |
| uncertainty* | number | |
| removal_sets* | array | Unique sorted sets of optional original task indices; include the empty set, preserve required tasks, and keep at least one task. |
| extra_minutes* | array | Unique permitted deadline increments; include zero and keep every modified deadline at most 1440 minutes. |
| duration_model* |
Survey up to 512 initial orbits in a planar circular Sun–Jupiter model; at most 4 million reserved CPU steps. Return finite-window sensitivity, actual durations, sampled Jacobi drift and explicit stops. Bands do not prove chaos or stability; radial overlap is not an encounter. Direct-only.
| Argument | Type | Description |
|---|---|---|
| n_a* | integer | |
| n_e* | integer | |
| e_max* | number | |
| e_min* | number | |
| a_max_au* | number | |
| a_min_au* | number | |
| mass_ratio | number | |
| duration_yr | number | |
| max_work_units | integer | |
Read native contracts, themes, units, assumptions, backends and approved composition families; optional exact theme filter. tools/list discovers direct MCP tools; list_composition_capabilities adds planner bindings.
| Argument | Type | Description |
|---|---|---|
| theme | string |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"theme": {
"type": "string",
"maxLength": 64,
"minLength": 1
}
},
"additionalProperties": false
}Read implemented versioned contracts, native capabilities, approved adapters and planning examples. Unsupported unit/model facts expose missing adapters. No engines run; direct tools remain independently callable.
No arguments.
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {},
"additionalProperties": false
}Read contributor availability, offered CPU/GPU resources and verified throughput by workload. Hardware is self-reported; per-GPU VRAM is not pooled. Mixed-workload samples do not measure comparative speed.
No arguments.
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {},
"additionalProperties": false
}Exactly maximize value for up to 32 independent, indivisible tasks within an integer-minute budget. Each task is selected at most once; no prerequisites or shared resources.
| Argument | Type | Description |
|---|---|---|
| items* | array | |
| budget* | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"budget",
"items"
],
"properties": {
"items": {
"type": "array",
"items": {
"type": "object",
"required": [
"name",
"duration",
"value"
],
"properties": {
"name": {
"type": "string",
"maxLength": 120,
"minLength": 1
},
"value": {
"type": "integer",
"maximum": 10000,
"minimum": 0
},
"duration": {
"type": "integer",
"maximum": 1440,
"minimum": 1
}
}
},
"maxItems": 32,
"minItems": 1
},
"budget": {
"type": "integer",
"maximum": 1440,
"minimum": 1
}
}
}Compute geometric golden [-4,+6°] and blue [-6,-4°] windows for one UTC day, 1900–2100. Sunrise at -0.833° is a separate convention. No refraction, terrain or weather. Numerical tolerance is not astronomical accuracy; oracle validation covers reference dates only. Shared solar models are not independent corroboration.
| Argument | Type | Description |
|---|---|---|
| date_utc* | string | Real Gregorian UTC midnight, year 1900–2100. Rust also validates month/day and leap years. Other hours are rejected, never truncated; this is not a local civil day. |
| latitude* | number | Degrees, North positive. |
| longitude* | number | Degrees, East positive. |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"date_utc",
"latitude",
"longitude"
],
"properties": {
"date_utc": {
"type": "string",
"pattern": "^(?:19\\d{2}|20\\d{2}|2100)-\\d{2}-\\d{2}T00:00:00Z$",
"maxLength": 20,
"minLength": 20,
"description": "Real Gregorian UTC midnight, year 1900–2100. Rust also validates month/day and leap years. Other hours are rejected, never truncated; this is not a local civil day."
},
"latitude": {
"type": "number",
"maximum": 89,
"minimum": -89,
"description": "Degrees, North positive."
},
"longitude": {
"type": "number",
"maximum": 180,
"minimum": -180,
"description": "Degrees, East positive."
}
},
"additionalProperties": false
}Preview robust scheduling without running engines: validate assumptions/permissions and return up to three candidate budgets (nominal, 10% reserve, 20% reserve), compute limits or blockers. No arbitrary tools or external code.
| Argument | Type | Description |
|---|---|---|
| seed | integer | |
| items* | array | |
| budget* | integer | |
| samples | integer | |
| uncertainty* | number | |
| allowed_tools | array | |
| duration_model | string | |
| max_candidates | integer | |
| min_success_rate | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"items",
"budget",
"uncertainty"
],
"properties": {
"seed": {
"type": "integer",
"default": 42,
"maximum": 4294967295,
"minimum": 0
},
"items": {
"type": "array",
"items": {
"type": "object",
"required": [
"name",
"duration",
"value"
],
"properties": {
"name": {
"type": "string",
"maxLength": 120,
"minLength": 1
},
"value": {
"type": "integer",
"maximum": 10000,
"minimum": 0
},
"duration": {
"type": "integer",
"maximum": 1440,
"minimum": 1
}
},
"additionalProperties": false
},
"maxItems": 32,
"minItems": 1
},
"budget": {
"type": "integer",
"maximum": 1440,
"minimum": 1
},
"samples": {
"type": "integer",
"default": 10000,
"maximum": 20000,
"minimum": 100
},
"uncertainty": {
"type": "number",
"maximum": 0.5,
"minimum": 0
},
"allowed_tools": {
"type": "array",
"items": {
"type": "string",
"pattern": "^[a-z][a-z0-9_]*$",
"maxLength": 64,
"minLength": 1
},
"default": [
"optimize_tasks",
"simulate_plan"
],
"maxItems": 14
},
"duration_model": {
"type": "string",
"default": "independent_uniform",
"maxLength": 64,
"minLength": 1
},
"max_candidates": {
"type": "integer",
"default": 3,
"maximum": 3,
"minimum": 1
},
"min_success_rate": {
"type": "number",
"default": 0.95,
"maximum": 0.999,
"minimum": 0.5
}
},
"additionalProperties": false
}Fit original tracks, then rank 1–64 supplied future series by local-linear uncertainty and declared cost. Assumes constant velocity, independent new errors and exact stations/clocks. Candidate angles and client baselines are forbidden. Prediction is not an acquired measurement or visibility proof.
| Argument | Type | Description |
|---|---|---|
| objective* | object | |
| candidates* | array | |
| assumptions* | object | |
| constraints* | object | |
| observations* | object | Original angular observations; Rust computes the baseline fit and covariance itself. |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"observations",
"candidates",
"objective",
"constraints",
"assumptions"
],
"properties": {
"objective": {
"type": "object",
"required": [
"horizon_s"
],
"properties": {
"horizon_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Absolute comparison time in the same corrected seconds as the observations; after the original observations, within their bounded 3600-second domain."
}
},
"additionalProperties": false
},
"candidates": {
"type": "array",
"items": {
"type": "object",
"required": [
"id",
"station",
"sample_times_s",
"sigma_az_deg",
"sigma_el_deg",
"cost_units"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[A-Za-z0-9_.-]+$",
"maxLength": 64,
"minLength": 1
},
"station": {
"type": "object",
"required": [
"id",
"lat",
"lon",
"elevation_m"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[A-Za-z0-9_.-]+$",
"maxLength": 64,
"minLength": 1
},
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"elevation_m": {
"type": "number",
"maximum": 9000,
"minimum": -500
}
},
"additionalProperties": false
},
"cost_units": {
"type": "number",
"maximum": 1000000000,
"minimum": 0
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sample_times_s": {
"type": "array",
"items": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000
},
"maxItems": 120,
"minItems": 3,
"description": "Proposed corrected times, strictly increasing, after the last original observation and no later than the common horizon. No measured or simulated angles are accepted here."
}
},
"additionalProperties": false
},
"maxItems": 64,
"minItems": 1
},
"assumptions": {
"type": "object",
"required": [
"independent_new_errors",
"exact_stations_and_clocks",
"constant_velocity"
],
"properties": {
"constant_velocity": {
"type": "boolean",
"const": true
},
"independent_new_errors": {
"type": "boolean",
"const": true
},
"exact_stations_and_clocks": {
"type": "boolean",
"const": true
}
},
"additionalProperties": false
},
"constraints": {
"type": "object",
"required": [
"max_cost_units",
"min_elevation_deg"
],
"properties": {
"max_cost_units": {
"type": "number",
"maximum": 1000000000,
"minimum": 0
},
"min_elevation_deg": {
"type": "number",
"maximum": 89,
"minimum": -2
}
},
"additionalProperties": false
},
"observations": {
"type": "object",
"required": [
"observers"
],
"properties": {
"observers": {
"type": "array",
"items": {
"type": "object",
"required": [
"lat",
"lon",
"sigma_az_deg",
"sigma_el_deg",
"samples"
],
"properties": {
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"t_s",
"azimuth_deg",
"elevation_deg"
],
"properties": {
"t_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Seconds from a common epoch, strictly increasing for this observer."
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -2
}
},
"additionalProperties": false
},
"maxItems": 120,
"minItems": 3
},
"elevation_m": {
"type": "number",
"default": 0,
"maximum": 9000,
"minimum": -500
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"clock_offset_s": {
"type": "number",
"default": 0,
"maximum": 60,
"minimum": -60,
"description": "The observer clock is ahead of the common base by this many seconds; the engine subtracts it."
}
},
"additionalProperties": false
},
"maxItems": 4,
"minItems": 2
}
},
"description": "Original angular observations; Rust computes the baseline fit and covariance itself.",
"additionalProperties": false
}
},
"additionalProperties": false
}Check dimensions, then compare first-order GUM with seeded fixed-sample Monte Carlo for an explicit model of 1–16 inputs. Return uncertainty budgets, coverage intervals and convergence/linearization findings. Conditional on supplied distributions; no affine units. CPU, direct-only; no planner binding.
| Argument | Type | Description |
|---|---|---|
| seed | integer | Default 1. Same seed, same result. |
| samples | integer | Monte Carlo draws, default 1000000 (JCGM 101 typical value for 2 significant digits). |
| coverage | number | Coverage probability, default 0.95. |
| variables* | array | |
| expression* | string | Model with + - * / ^, parentheses, pi and sqrt exp ln log10 sin cos tan asin acos atan abs. Literals are dimensionless; no implicit multiplication. |
| result_unit | string | Output unit; must match the model dimension. |
| correlations | array | Correlations between normal inputs with standard_uncertainty > 0. |
Order 2–256 points from index 0 using planar or spherical kilometre distances. Exact only after completed Held–Karp search (at most 13 points); otherwise bounded heuristics. Returns every leg and stop reason. No roads or traffic.
| Argument | Type | Description |
|---|---|---|
| metric* | string | |
| points* | array | |
| time_budget_ms | integer | |
| return_to_start | boolean |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"metric",
"points"
],
"properties": {
"metric": {
"enum": [
"euclidean_km",
"great_circle_km"
],
"type": "string"
},
"points": {
"type": "array",
"items": {
"anyOf": [
{
"type": "object",
"required": [
"x",
"y"
],
"properties": {
"x": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"y": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
}
},
"additionalProperties": false
},
{
"type": "object",
"required": [
"lat",
"lon"
],
"properties": {
"lat": {
"type": "number",
"maximum": 90,
"minimum": -90
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
}
},
"additionalProperties": false
}
]
},
"maxItems": 256,
"minItems": 2
},
"time_budget_ms": {
"type": "integer",
"default": 1000,
"maximum": 10000,
"minimum": 100
},
"return_to_start": {
"type": "boolean",
"default": true
}
},
"additionalProperties": false
}Execute a supplied bounded score AST on 2–128 Euclidean-km points with depot 0 and 2-opt. Validates the closed tour; exact=false. No retraining, external effects or promotion. Hashes identify programs, not independent validation.
| Argument | Type | Description |
|---|---|---|
| points* | array | |
| program* | object | |
| fuel_limit | integer | |
| time_budget_ms | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"points",
"program"
],
"properties": {
"points": {
"type": "array",
"items": {
"type": "object",
"required": [
"x",
"y"
],
"properties": {
"x": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"y": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
}
},
"additionalProperties": false
},
"maxItems": 128,
"minItems": 2
},
"program": {
"type": "object",
"required": [
"version",
"score"
],
"properties": {
"score": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"left": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"left": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"left": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"left": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"value": {
"anyOf": [
{
"type": "number",
"const": -2
},
{
"type": "number",
"const": -1
},
{
"type": "number",
"const": -0.5
},
{
"type": "number",
"const": 0
},
{
"type": "number",
"const": 0.5
},
{
"type": "number",
"const": 1
},
{
"type": "number",
"const": 2
}
]
}
},
"additionalProperties": false
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"right": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"value": {
"anyOf": [
{
"type": "number",
"const": -2
},
{
"type": "number",
"const": -1
},
{
"type": "number",
"const": -0.5
},
{
"type": "number",
"const": 0
},
{
"type": "number",
"const": 0.5
},
{
"type": "number",
"const": 1
},
{
"type": "number",
"const": 2
}
]
}
},
"additionalProperties": false
},
"value": {
"anyOf": [
{
"type": "number",
"const": -2
},
{
"type": "number",
"const": -1
},
{
"type": "number",
"const": -0.5
},
{
"type": "number",
"const": 0
},
{
"type": "number",
"const": 0.5
},
{
"type": "number",
"const": 1
},
{
"type": "number",
"const": 2
}
]
}
},
"additionalProperties": false
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"right": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"left": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"value": {
"anyOf": [
{
"type": "number",
"const": -2
},
{
"type": "number",
"const": -1
},
{
"type": "number",
"const": -0.5
},
{
"type": "number",
"const": 0
},
{
"type": "number",
"const": 0.5
},
{
"type": "number",
"const": 1
},
{
"type": "number",
"const": 2
}
]
}
},
"additionalProperties": false
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"right": {
"type": "object",
"required": [
"op"
],
"properties": {
"op": {
"enum": [
"feature",
"constant",
"add",
"sub",
"mul",
"min",
"max"
],
"type": "string"
},
"name": {
"enum": [
"distance",
"depot",
"isolation",
"centrality",
"progress"
],
"type": "string"
},
"value": {
"anyOf": [
{
"type": "number",
"const": -2
},
{
"type": "number",
"const": -1
},
{
"type": "number",
"const": -0.5
},
{
"type": "number",
"const": 0
},
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"type": "integer",
"default": 2000000,
"maximum": 4000000,
"minimum": 1
},
"time_budget_ms": {
"type": "integer",
"default": 100,
"maximum": 1000,
"minimum": 100
}
},
"additionalProperties": false
}Bounded deterministic float64 scan of a scalar <= or >= claim over a declared grid of 1–6 variables. Reports numerical witnesses, undefined and uncertain evaluations, and the exact stop reason. A propagated screening guard rejects near-boundary candidates; it is not a certified interval or formal proof. An inconclusive outcome preserves unresolved sampled cells; absence of a witness does not establish the claim over the continuous box.
| Argument | Type | Description |
|---|---|---|
| bound* | number | |
| relation* | any | |
| tolerance | number | |
| variables* | array | |
| expression* | string | |
| max_evaluations | integer | |
| max_counterexamples | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"bound",
"expression",
"relation",
"variables"
],
"properties": {
"bound": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000
},
"relation": {
"anyOf": [
{
"type": "string",
"const": "le"
},
{
"type": "string",
"const": "ge"
}
]
},
"tolerance": {
"type": "number",
"maximum": 1000000000000,
"minimum": 0
},
"variables": {
"type": "array",
"items": {
"type": "object",
"required": [
"max",
"min",
"name",
"steps"
],
"properties": {
"max": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"min": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"name": {
"type": "string",
"pattern": "^[A-Za-z_][A-Za-z0-9_]*$",
"maxLength": 32,
"minLength": 1
},
"steps": {
"type": "integer",
"maximum": 64,
"minimum": 2
}
},
"additionalProperties": false
},
"maxItems": 6,
"minItems": 1
},
"expression": {
"type": "string",
"maxLength": 512,
"minLength": 1
},
"max_evaluations": {
"type": "integer",
"maximum": 200000,
"minimum": 1
},
"max_counterexamples": {
"type": "integer",
"maximum": 16,
"minimum": 1
}
},
"additionalProperties": false
}Screen a supplied trade series for repeated volume at nearly equal prices within a declared time window. Return recycled-volume ratio and cycles; a pattern does not prove wash trading.
| Argument | Type | Description |
|---|---|---|
| trades* | array | |
| window_s | number | |
| price_band_pct | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"trades"
],
"properties": {
"trades": {
"type": "array",
"items": {
"type": "object",
"required": [
"ts_s",
"price",
"volume"
],
"properties": {
"ts_s": {
"type": "number",
"minimum": 0
},
"price": {
"type": "number",
"minimum": 0
},
"volume": {
"type": "number",
"minimum": 0
}
}
},
"maxItems": 5000,
"minItems": 20
},
"window_s": {
"type": "number",
"default": 3600,
"maximum": 86400,
"minimum": 60
},
"price_band_pct": {
"type": "number",
"default": 0.25,
"maximum": 5,
"minimum": 0.01
}
}
}Kac's question in reverse: design a polygonal drumhead whose lowest tones play requested frequency ratios (a fifth, a triad, a pentatonic scale), each accepted within ±tolerance_cents. proven_impossible is returned only when proven theorems exclude every ratio combination inside those tolerance windows for a connected uniform membrane with a fixed edge: simple fundamental, f2/f1 ≤ j11/j01 ≈ 1.5933 with equality for the disk (Ashbaugh–Benguria 1992), and Yang's universal inequality minimized exactly over the window box; an exact-target exclusion is reported separately. Otherwise multi-start L-BFGS with exact finite-element shape derivatives designs a 5–16-vertex polygon, then reanalyses it on three refined meshes with the shared hear_the_shape solver: achieved ratios, errors in cents with estimated uncertainty (not rigorous bounds), resolution warnings, optional numerical tuning of the fundamental in Hz. not_achieved is a bounded-search result, never an impossibility proof. Ideal membrane only.
| Argument | Type | Description |
|---|---|---|
| seed | integer | Default 1. Same seed, same drum. |
| vertices | integer | Polygon vertices, default 10. |
| wave_speed | number | m/s, √(tension/areal density). |
| target_ratios* | array | Frequency ratios f2/f1, f3/f1, … of the lowest modes, ascending (e.g. [1.25, 1.5] for a just major triad). |
| fundamental_hz | number | With wave_speed: scale the drum so its fundamental sounds at this frequency. |
Estimate pi with seeded Monte Carlo and a 95% Wilson interval; up to 5 million samples. CPU or optional CUDA. Other direct scientific engines run on CPU.
| Argument | Type | Description |
|---|---|---|
| seed* | integer | |
| backend | string | |
| samples* | integer | |
| device_ids | array |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"samples",
"seed"
],
"properties": {
"seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0
},
"backend": {
"enum": [
"cpu",
"cuda"
],
"type": "string",
"default": "cpu"
},
"samples": {
"type": "integer",
"maximum": 5000000,
"minimum": 100
},
"device_ids": {
"type": "array",
"items": {
"type": "integer",
"maximum": 9007199254740991,
"minimum": 0
},
"maxItems": 16
}
}
}Estimate deadline success, mean duration and empirical p95 for up to 32 integer-minute tasks under independent bounded uniform duration variations. Seeded CPU sampling; not a real-world forecast guarantee.
| Argument | Type | Description |
|---|---|---|
| seed* | integer | |
| budget* | integer | |
| samples* | integer | |
| durations* | array | |
| uncertainty* | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"durations",
"budget",
"samples",
"seed",
"uncertainty"
],
"properties": {
"seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0
},
"budget": {
"type": "integer",
"maximum": 1440,
"minimum": 1
},
"samples": {
"type": "integer",
"maximum": 100000,
"minimum": 100
},
"durations": {
"type": "array",
"items": {
"type": "integer",
"maximum": 1440,
"minimum": 1
},
"maxItems": 32,
"minItems": 1
},
"uncertainty": {
"type": "number",
"maximum": 0.5,
"minimum": 0
}
}
}Solve Kuhn poker with CFR+ self-play, measure exploitability with pure best responses and compare the game value with -1/18. Illustrative game theory, not gambling advice.
| Argument | Type | Description |
|---|---|---|
| iterations | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"iterations": {
"type": "integer",
"default": 200000,
"maximum": 5000000,
"minimum": 1000
}
}
}Refit 1–32 declared hypothetical angular/clock perturbations to challenge reconstruction stability. Explicit hypothetical acknowledgement required. Non-convergence is inconclusive; none_found covers examined cases only. No new observations.
| Argument | Type | Description |
|---|---|---|
| cases* | array | |
| claim* | object | |
| bounds* | object | |
| observations* | object | |
| perturbations_are_hypothetical* | boolean |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"observations",
"claim",
"bounds",
"cases",
"perturbations_are_hypothetical"
],
"properties": {
"cases": {
"type": "array",
"items": {
"type": "object",
"required": [
"id",
"observer_index",
"azimuth_bias_deg",
"elevation_bias_deg",
"clock_offset_delta_s"
],
"properties": {
"id": {
"type": "string",
"pattern": "^[A-Za-z0-9_-]+$",
"maxLength": 64,
"minLength": 1
},
"observer_index": {
"type": "integer",
"maximum": 3,
"minimum": 0
},
"azimuth_bias_deg": {
"type": "number",
"maximum": 10,
"minimum": -10
},
"elevation_bias_deg": {
"type": "number",
"maximum": 10,
"minimum": -10
},
"clock_offset_delta_s": {
"type": "number",
"maximum": 60,
"minimum": -60,
"description": "Hypothetical change to the declared clock correction, not to the measured timestamps."
}
},
"additionalProperties": false
},
"maxItems": 32,
"minItems": 1
},
"claim": {
"type": "object",
"required": [
"evaluation_time_s",
"max_position_shift_m"
],
"properties": {
"evaluation_time_s": {
"type": "number",
"description": "Absolute corrected time, within 3600 seconds of the first corrected original measurement."
},
"max_position_shift_m": {
"type": "number",
"maximum": 1000000,
"minimum": 0.001
}
},
"additionalProperties": false
},
"bounds": {
"type": "object",
"required": [
"max_angular_bias_deg",
"max_clock_offset_delta_s",
"max_evaluations",
"stop_on_first"
],
"properties": {
"stop_on_first": {
"type": "boolean"
},
"max_evaluations": {
"type": "integer",
"maximum": 32,
"minimum": 1
},
"max_angular_bias_deg": {
"type": "number",
"maximum": 10,
"minimum": 0
},
"max_clock_offset_delta_s": {
"type": "number",
"maximum": 60,
"minimum": 0
}
},
"additionalProperties": false
},
"observations": {
"type": "object",
"required": [
"observers"
],
"properties": {
"observers": {
"type": "array",
"items": {
"type": "object",
"required": [
"lat",
"lon",
"sigma_az_deg",
"sigma_el_deg",
"samples"
],
"properties": {
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"t_s",
"azimuth_deg",
"elevation_deg"
],
"properties": {
"t_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Seconds from a common epoch, strictly increasing for this observer."
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -2
}
},
"additionalProperties": false
},
"maxItems": 120,
"minItems": 3
},
"elevation_m": {
"type": "number",
"default": 0,
"maximum": 9000,
"minimum": -500
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"clock_offset_s": {
"type": "number",
"default": 0,
"maximum": 60,
"minimum": -60,
"description": "The observer clock is ahead of the common base by this many seconds; the engine subtracts it."
}
},
"additionalProperties": false
},
"maxItems": 4,
"minItems": 2
}
},
"additionalProperties": false
},
"perturbations_are_hypothetical": {
"type": "boolean",
"const": true
}
},
"additionalProperties": false
}Queue fixed public synthetic pi (CPU/CUDA) or one of three discrete schedule scenarios (CPU only). No private data/custom code. Returns a ticket; poll get_network_job. Coordinator recomputes every accepted shard; no net speedup claim. Jobs may expire.
| Argument | Type | Description |
|---|---|---|
| seed | integer | |
| backend | string | |
| samples* | integer | |
| workload | string | |
| scenario_id | string |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"samples"
],
"properties": {
"seed": {
"type": "integer",
"default": 42,
"maximum": 4294967295,
"minimum": 0
},
"backend": {
"enum": [
"auto",
"cpu",
"cuda"
],
"type": "string",
"default": "auto"
},
"samples": {
"type": "integer",
"maximum": 5000000,
"minimum": 100
},
"workload": {
"enum": [
"pi_chunk_v1",
"schedule_probe_v1"
],
"type": "string",
"default": "pi_chunk_v1"
},
"scenario_id": {
"enum": [
"single_80_deadline_90",
"pair_60_40_deadline_100",
"pair_60_40_deadline_110"
],
"type": "string"
}
},
"additionalProperties": false
}Locally normalized geometric descriptors of 3–256 planar points: distances, nearest-neighbour isolation, centroid spread, PCA collinearity and histogram. The principal-axis mirror residual is null for isotropic noncoincident covariance, whose axes are undetermined. Rounded fingerprints are descriptive, not proofs of equivalence or method benefit.
| Argument | Type | Description |
|---|---|---|
| points* | array | |
| reference_distance_fraction | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"points"
],
"properties": {
"points": {
"type": "array",
"items": {
"type": "object",
"required": [
"x",
"y"
],
"properties": {
"x": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
},
"y": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000
}
},
"additionalProperties": false
},
"maxItems": 256,
"minItems": 3
},
"reference_distance_fraction": {
"type": "number",
"maximum": 0.5,
"minimum": 0.01
}
},
"additionalProperties": false
}Fit position/velocity from 2–4 supplied azimuth/elevation tracks using constant velocity in spherical ECEF and declared angular noise/clocks. Reports fit status and conditional local uncertainty; no object identification or calibrated accuracy.
| Argument | Type | Description |
|---|---|---|
| observers* | array |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"observers"
],
"properties": {
"observers": {
"type": "array",
"items": {
"type": "object",
"required": [
"lat",
"lon",
"sigma_az_deg",
"sigma_el_deg",
"samples"
],
"properties": {
"lat": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"lon": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"samples": {
"type": "array",
"items": {
"type": "object",
"required": [
"t_s",
"azimuth_deg",
"elevation_deg"
],
"properties": {
"t_s": {
"type": "number",
"maximum": 1000000000000,
"minimum": -1000000000000,
"description": "Seconds from a common epoch, strictly increasing for this observer."
},
"azimuth_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"elevation_deg": {
"type": "number",
"maximum": 90,
"minimum": -2
}
},
"additionalProperties": false
},
"maxItems": 120,
"minItems": 3
},
"elevation_m": {
"type": "number",
"default": 0,
"maximum": 9000,
"minimum": -500
},
"sigma_az_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"sigma_el_deg": {
"type": "number",
"maximum": 10,
"minimum": 0.01
},
"clock_offset_s": {
"type": "number",
"default": 0,
"maximum": 60,
"minimum": -60,
"description": "The observer clock is ahead of the common base by this many seconds; the engine subtracts it."
}
},
"additionalProperties": false
},
"maxItems": 4,
"minItems": 2
}
},
"additionalProperties": false
}Verify a structured arithmetic, shadow, ephemeris, statistics or route claim with a bounded native engine. Returns a model-scoped verdict and portable Ed25519 server receipt; never truth, authenticity or fraud certification. Route claims explicitly distinguish optimality from a supplied tour total. Native failures return no scientific verdict. Parameters and examples: /verify and /docs/mcp/.
| Argument | Type | Description |
|---|---|---|
| claim | object | |
| domain* | string | |
| parameters* | object |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"domain",
"parameters"
],
"properties": {
"claim": {
"type": "object",
"required": [
"kind",
"claimed_total_km"
],
"properties": {
"kind": {
"enum": [
"optimality",
"tour_total"
],
"type": "string"
},
"order": {
"type": "array",
"items": {
"type": "integer",
"maximum": 255,
"minimum": 0
},
"maxItems": 256,
"minItems": 2
},
"claimed_total_km": {
"type": "number",
"maximum": 1000000000000,
"minimum": 0
}
},
"additionalProperties": false
},
"domain": {
"enum": [
"numbers",
"shadow",
"ephemeris",
"statistics",
"route"
],
"type": "string"
},
"parameters": {
"type": "object",
"propertyNames": {
"type": "string"
},
"additionalProperties": {}
}
},
"additionalProperties": false
}Check measured shadows using NOAA solar position, a ground-plane homography from 4–16 controls and Monte Carlo uncertainty. Returns conditional consistency, never image authenticity.
| Argument | Type | Description |
|---|---|---|
| seed | integer | |
| shadow* | object | |
| samples | integer | |
| date_utc* | string | |
| latitude* | number | |
| longitude* | number | |
| pixel_sigma | number | |
| second_shadow | object | |
| control_points* | array | |
| time_sigma_minutes | number |
| string |
| deadline_minutes* | integer |
| min_success_rate* | number |
| required_indices* | array |
| confirmation_seed* | integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"items",
"required_indices",
"deadline_minutes",
"extra_minutes",
"removal_sets",
"costs",
"uncertainty",
"min_success_rate",
"samples",
"search_seed",
"confirmation_seed",
"duration_model"
],
"properties": {
"costs": {
"type": "object",
"required": [
"per_extra_minute",
"per_lost_value",
"max_cost"
],
"properties": {
"max_cost": {
"type": "number",
"maximum": 1000000000000,
"minimum": 0
},
"per_lost_value": {
"type": "number",
"maximum": 1000000,
"exclusiveMinimum": 0
},
"per_extra_minute": {
"type": "number",
"maximum": 1000000,
"exclusiveMinimum": 0
}
},
"additionalProperties": false
},
"items": {
"type": "array",
"items": {
"type": "object",
"required": [
"name",
"duration",
"value"
],
"properties": {
"name": {
"type": "string",
"maxLength": 120,
"minLength": 1
},
"value": {
"type": "integer",
"maximum": 10000,
"minimum": 0
},
"duration": {
"type": "integer",
"maximum": 1440,
"minimum": 1
}
},
"additionalProperties": false
},
"maxItems": 32,
"minItems": 1
},
"samples": {
"type": "integer",
"maximum": 10000,
"minimum": 100
},
"search_seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0
},
"uncertainty": {
"type": "number",
"maximum": 0.5,
"minimum": 0
},
"removal_sets": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"maximum": 31,
"minimum": 0
},
"maxItems": 31
},
"maxItems": 32,
"minItems": 1,
"description": "Unique sorted sets of optional original task indices; include the empty set, preserve required tasks, and keep at least one task."
},
"extra_minutes": {
"type": "array",
"items": {
"type": "integer",
"maximum": 1439,
"minimum": 0
},
"maxItems": 32,
"minItems": 1,
"description": "Unique permitted deadline increments; include zero and keep every modified deadline at most 1440 minutes."
},
"duration_model": {
"type": "string",
"const": "independent_uniform"
},
"deadline_minutes": {
"type": "integer",
"maximum": 1440,
"minimum": 1
},
"min_success_rate": {
"type": "number",
"maximum": 1,
"minimum": 0.5
},
"required_indices": {
"type": "array",
"items": {
"type": "integer",
"maximum": 31,
"minimum": 0
},
"maxItems": 32
},
"confirmation_seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0
}
},
"additionalProperties": false
}| steps_per_year |
| integer |
| initial_phase_deg | number |
| jupiter_semi_major_au | number |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"a_max_au",
"a_min_au",
"e_max",
"e_min",
"n_a",
"n_e"
],
"properties": {
"n_a": {
"type": "integer",
"maximum": 64,
"minimum": 2
},
"n_e": {
"type": "integer",
"maximum": 64,
"minimum": 2
},
"e_max": {
"type": "number",
"maximum": 0.7,
"minimum": 0
},
"e_min": {
"type": "number",
"maximum": 0.7,
"minimum": 0
},
"a_max_au": {
"type": "number",
"maximum": 5.6,
"minimum": 1.5
},
"a_min_au": {
"type": "number",
"maximum": 5.5,
"minimum": 1.5
},
"mass_ratio": {
"type": "number",
"maximum": 0.04,
"minimum": 0.000001
},
"duration_yr": {
"type": "number",
"maximum": 5000,
"minimum": 50
},
"max_work_units": {
"type": "integer",
"maximum": 4000000,
"minimum": 10000
},
"steps_per_year": {
"type": "integer",
"maximum": 128,
"minimum": 8
},
"initial_phase_deg": {
"type": "number",
"maximum": 360,
"minimum": 0
},
"jupiter_semi_major_au": {
"type": "number",
"maximum": 8,
"minimum": 3
}
},
"additionalProperties": false
}{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"expression",
"variables"
],
"properties": {
"seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0,
"description": "Default 1. Same seed, same result."
},
"samples": {
"type": "integer",
"maximum": 2000000,
"minimum": 10000,
"description": "Monte Carlo draws, default 1000000 (JCGM 101 typical value for 2 significant digits)."
},
"coverage": {
"type": "number",
"maximum": 0.999,
"minimum": 0.5,
"description": "Coverage probability, default 0.95."
},
"variables": {
"type": "array",
"items": {
"type": "object",
"required": [
"distribution",
"name",
"value"
],
"properties": {
"name": {
"type": "string",
"pattern": "^[A-Za-z_][A-Za-z0-9_]*$",
"maxLength": 32,
"minLength": 1
},
"unit": {
"type": "string",
"maxLength": 64,
"minLength": 0,
"description": "e.g. mg, km/h, kg/m^3, W/m^2/K, deg, kWh, %. Empty means dimensionless. °C and °F are refused; use K."
},
"value": {
"type": "number",
"maximum": 1e+300,
"minimum": -1e+300,
"description": "Best estimate, in unit."
},
"half_width": {
"type": "number",
"maximum": 1e+300,
"minimum": 0,
"description": "uniform and triangular only: half-width, in unit."
},
"distribution": {
"anyOf": [
{
"type": "string",
"const": "constant"
},
{
"type": "string",
"const": "normal"
},
{
"type": "string",
"const": "uniform"
},
{
"type": "string",
"const": "triangular"
}
]
},
"standard_uncertainty": {
"type": "number",
"maximum": 1e+300,
"minimum": 0,
"description": "normal only: standard deviation, in unit."
}
},
"additionalProperties": false
},
"maxItems": 16,
"minItems": 1
},
"expression": {
"type": "string",
"maxLength": 512,
"minLength": 1,
"description": "Model with + - * / ^, parentheses, pi and sqrt exp ln log10 sin cos tan asin acos atan abs. Literals are dimensionless; no implicit multiplication."
},
"result_unit": {
"type": "string",
"maxLength": 64,
"minLength": 1,
"description": "Output unit; must match the model dimension."
},
"correlations": {
"type": "array",
"items": {
"type": "object",
"required": [
"a",
"b",
"coefficient"
],
"properties": {
"a": {
"type": "string",
"maxLength": 32,
"minLength": 1
},
"b": {
"type": "string",
"maxLength": 32,
"minLength": 1
},
"coefficient": {
"type": "number",
"maximum": 1,
"minimum": -1
}
},
"additionalProperties": false
},
"maxItems": 64,
"minItems": 0,
"description": "Correlations between normal inputs with standard_uncertainty > 0."
}
},
"additionalProperties": false
}| max_evaluations | integer | Search budget in finite-element evaluations, default 300. |
| tolerance_cents | number | Success when |error| + uncertainty ≤ tolerance for every ratio; default 5 cents. |
| include_mode_shapes | boolean | Adds computed mode shapes from the shared forward solver (≤1024 triangles, full-precision coordinates) for visualization. |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"target_ratios"
],
"properties": {
"seed": {
"type": "integer",
"maximum": 4294967295,
"minimum": 0,
"description": "Default 1. Same seed, same drum."
},
"vertices": {
"type": "integer",
"maximum": 16,
"minimum": 5,
"description": "Polygon vertices, default 10."
},
"wave_speed": {
"type": "number",
"maximum": 1000000,
"minimum": 1e-9,
"description": "m/s, √(tension/areal density)."
},
"target_ratios": {
"type": "array",
"items": {
"type": "number",
"maximum": 4,
"minimum": 1
},
"maxItems": 5,
"minItems": 1,
"description": "Frequency ratios f2/f1, f3/f1, … of the lowest modes, ascending (e.g. [1.25, 1.5] for a just major triad)."
},
"fundamental_hz": {
"type": "number",
"maximum": 20000,
"minimum": 1,
"description": "With wave_speed: scale the drum so its fundamental sounds at this frequency."
},
"max_evaluations": {
"type": "integer",
"maximum": 1000,
"minimum": 50,
"description": "Search budget in finite-element evaluations, default 300."
},
"tolerance_cents": {
"type": "number",
"maximum": 100,
"minimum": 0.5,
"description": "Success when |error| + uncertainty ≤ tolerance for every ratio; default 5 cents."
},
"include_mode_shapes": {
"type": "boolean",
"description": "Adds computed mode shapes from the shared forward solver (≤1024 triangles, full-precision coordinates) for visualization."
}
},
"additionalProperties": false
}{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"required": [
"date_utc",
"latitude",
"longitude",
"control_points",
"shadow"
],
"properties": {
"seed": {
"type": "integer",
"default": 7,
"maximum": 4294967295,
"minimum": 0
},
"shadow": {
"type": "object",
"required": [
"a",
"b"
],
"properties": {
"a": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
},
"b": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
}
}
},
"samples": {
"type": "integer",
"default": 2000,
"maximum": 20000,
"minimum": 100
},
"date_utc": {
"type": "string",
"maxLength": 20,
"minLength": 20
},
"latitude": {
"type": "number",
"maximum": 89,
"minimum": -89
},
"longitude": {
"type": "number",
"maximum": 180,
"minimum": -180
},
"pixel_sigma": {
"type": "number",
"default": 3,
"maximum": 50,
"minimum": 0
},
"second_shadow": {
"type": "object",
"required": [
"a",
"b"
],
"properties": {
"a": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
},
"b": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
}
}
},
"control_points": {
"type": "array",
"items": {
"type": "object",
"required": [
"px",
"world"
],
"properties": {
"px": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
},
"world": {
"type": "array",
"items": [
{
"type": "number"
},
{
"type": "number"
}
],
"maxItems": 2,
"minItems": 2,
"additionalItems": false
}
}
},
"maxItems": 16,
"minItems": 4
},
"time_sigma_minutes": {
"type": "number",
"default": 1,
"maximum": 240,
"minimum": 0
}
}
}