Workflow Dependency Analysis
Find missing dependencies and cyclic components; derive stable parallel layers, critical path, earliest/latest timings and slack from a supplied task graph. Caller-estimated integer durations and unlimited parallel workers only; never executes tasks.
workflow-assurance · Operation ID: workflow-dag-analyze
Choose this operation when
- Find cycles and missing dependencies in an agent task DAG
- Plan parallel execution stages and estimate a workflow critical path
Outside this profile
- Resource-constrained scheduling or runtime prediction guarantees
- Executing, authorizing, or monitoring agent work
Exact release references
Static JSON contract · Markdown reference · Fixed example response
Complete input schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"tasks": {
"minItems": 1,
"maxItems": 100,
"type": "array",
"items": {
"type": "object",
"properties": {
"id": {
"type": "string",
"minLength": 1,
"maxLength": 80
},
"dependsOn": {
"default": [],
"maxItems": 100,
"type": "array",
"items": {
"type": "string",
"minLength": 1,
"maxLength": 80
}
},
"durationMs": {
"default": 0,
"type": "integer",
"minimum": 0,
"maximum": 86400000
}
},
"required": [
"id"
],
"additionalProperties": false
}
}
},
"required": [
"tasks"
],
"additionalProperties": false
}
Complete output-envelope schema
{
"type": "object",
"required": [
"operation",
"version",
"result",
"provenance"
],
"properties": {
"operation": {
"const": "workflow-dag-analyze",
"type": "string"
},
"version": {
"const": "0.29.0",
"type": "string"
},
"result": {
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"profile": {
"type": "string",
"const": "workflow-dag-v1"
},
"schedulable": {
"type": "boolean"
},
"topologicalOrder": {
"type": "array",
"items": {
"type": "string"
}
},
"layers": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "string"
}
}
},
"cycles": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "string"
}
}
},
"unresolvedTaskIds": {
"type": "array",
"items": {
"type": "string"
}
},
"criticalPath": {
"type": "array",
"items": {
"type": "string"
}
},
"makespanMs": {
"anyOf": [
{
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
{
"type": "null"
}
]
},
"timing": {
"type": "array",
"items": {
"type": "object",
"properties": {
"id": {
"type": "string"
},
"earliestStartMs": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
"earliestFinishMs": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
"latestStartMs": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
"slackMs": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
}
},
"required": [
"id",
"earliestStartMs",
"earliestFinishMs",
"latestStartMs",
"slackMs"
],
"additionalProperties": false
}
},
"assumptions": {
"type": "array",
"items": {
"type": "string"
}
},
"findings": {
"type": "array",
"items": {
"type": "object",
"properties": {
"code": {
"type": "string"
},
"severity": {
"type": "string",
"enum": [
"error",
"warning"
]
},
"path": {
"type": "string"
},
"message": {
"type": "string"
}
},
"required": [
"code",
"severity",
"path",
"message"
],
"additionalProperties": false
}
},
"findingCount": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
"errorCount": {
"type": "integer",
"minimum": 0,
"maximum": 9007199254740991
},
"truncated": {
"type": "boolean"
}
},
"required": [
"profile",
"schedulable",
"topologicalOrder",
"layers",
"cycles",
"unresolvedTaskIds",
"criticalPath",
"makespanMs",
"timing",
"assumptions",
"findings",
"findingCount",
"errorCount",
"truncated"
],
"additionalProperties": false
},
"provenance": {
"type": "object",
"required": [
"inputSha256",
"outputSha256",
"deterministic",
"externalRequests"
],
"properties": {
"inputSha256": {
"type": "string",
"pattern": "^[a-f0-9]{64}$"
},
"outputSha256": {
"type": "string",
"pattern": "^[a-f0-9]{64}$"
},
"deterministic": {
"const": true
},
"externalRequests": {
"const": 0
}
}
}
},
"additionalProperties": false
}
Fixed example
One accepted fixed example, not a custom-input trial. No operation runs when this static page is requested.
Example input
{
"tasks": [
{
"id": "fetch",
"durationMs": 100
},
{
"id": "summarize",
"dependsOn": [
"fetch"
],
"durationMs": 300
},
{
"id": "index",
"dependsOn": [
"fetch"
],
"durationMs": 200
},
{
"id": "publish",
"dependsOn": [
"summarize",
"index"
],
"durationMs": 50
}
]
}
Example response
{
"operation": "workflow-dag-analyze",
"version": "0.29.0",
"result": {
"profile": "workflow-dag-v1",
"schedulable": true,
"topologicalOrder": [
"fetch",
"index",
"summarize",
"publish"
],
"layers": [
[
"fetch"
],
[
"index",
"summarize"
],
[
"publish"
]
],
"cycles": [],
"unresolvedTaskIds": [],
"criticalPath": [
"fetch",
"summarize",
"publish"
],
"makespanMs": 450,
"timing": [
{
"id": "fetch",
"earliestStartMs": 0,
"earliestFinishMs": 100,
"latestStartMs": 0,
"slackMs": 0
},
{
"id": "index",
"earliestStartMs": 100,
"earliestFinishMs": 300,
"latestStartMs": 200,
"slackMs": 100
},
{
"id": "publish",
"earliestStartMs": 400,
"earliestFinishMs": 450,
"latestStartMs": 400,
"slackMs": 0
},
{
"id": "summarize",
"earliestStartMs": 100,
"earliestFinishMs": 400,
"latestStartMs": 100,
"slackMs": 0
}
],
"assumptions": [
"Durations are caller estimates in integer milliseconds",
"Unlimited parallel workers; no resource, retry, or network-time model"
],
"findings": [],
"findingCount": 0,
"errorCount": 0,
"truncated": false
},
"provenance": {
"inputSha256": "654c113aff490cf72c0ff1c9957cfdfa5f2471cd0437e341e58f2eb81483c0fc",
"outputSha256": "4079a937ef3a0f4766cb2c0b1319139fc1cb87d4c90150b9a422db21b9e53df9",
"deterministic": true,
"externalRequests": 0
}
}
Bounds and precision
JavaScript IEEE-754 numbers; use strings for large integer IDs/exact decimals where the schema accepts strings. No lossless numeric parsing.
{
"global": {
"requestBytes": 131072,
"responseBytes": 524288,
"jsonDepth": 32,
"jsonNodes": 20000,
"requestsPerMinute": 60,
"paidAttemptsPerMinute": 20,
"idempotencyHours": 24
},
"operation": {
"inputBytes": 100000,
"outputBytes": 400000,
"jsonNodes": 8000,
"depth": 20,
"findings": 200,
"quoteSearchCharacters": 4000000,
"quoteOccurrenceEvaluations": 200000,
"tasks": 100,
"dependencyEdges": 1000,
"durationMsPerTask": 86400000
}
}
Complete schemas, descriptions and cross-field validation may impose additional limits.
Proposed price and protocol definitions
{
"unit": "one successful operation call",
"proposedNominalUsd": "0.01",
"sixDecimalTokenBaseUnits": "10000",
"subscription": false,
"includesPayerWalletOrNetworkFees": false,
"liveQuoteVerified": false,
"condition": "Actual SDK challenge is authoritative only within the caller's explicit authorization; configured six-decimal token peg is an operator assertion, not a conversion guarantee."
}
Protocol definitions: x402, mpp. MPP uses Tempo charge. Paid MCP execution is unsupported. All runtime readiness is not evaluated in this build.
API path templates, not endpoints on this documentation host
{
"x402": "/v1/x402/workflow-dag-analyze",
"mpp": "/v1/mpp/workflow-dag-analyze"
}
Required headers
{
"Content-Type": "application/json",
"Idempotency-Key": "random 16–128 character operation identifier"
}
Actual SDK challenge amount, asset, network, recipient and wallet costs must pass independent authorization. Preserve identical key, body, protocol and credential on retries; on PAYMENT_UNCERTAIN stop and reconcile.
Execution profile and provider conditions
{
"deterministic": true,
"externalRequests": 0,
"maxExternalRequests": 0,
"resultSnapshotPersisted": false,
"fixedExampleIsIllustrativeSnapshot": false,
"requiresPayment": true,
"supportsMcpExecution": false
}
Deterministic supplied-input operation with no external requests or stored request/result bodies. Payment infrastructure retains payment metadata and hashes.
Failure handling
- HTTP 400: Malformed JSON, missing/invalid idempotency key, or payment identifier mismatch Correct the request before payment
- HTTP 402: Payment challenge or rejected payment Use official protocol SDK; inspect payment outcome before another payment
- HTTP 409: Idempotency conflict, duplicate proof, or PAYMENT_UNCERTAIN Keep original key, body, and proof; reconcile uncertainty with operator; never blindly repay
- HTTP 413: Input or generated output too large Reduce input; no payment attempted for validation failure
- HTTP 415: Unsupported media type or compression Send uncompressed application/json
- HTTP 422: Schema or service-specific semantic validation failure Correct input using returned error code; no payment attempted
- HTTP 429: Request/payment-attempt rate exceeded Wait for rate limit window; preserve existing payment identity
- HTTP 503: Payment configuration/provider/state unavailable, or live DNS preparation failed before settlement Check readiness; DNS preparation failures may retry the identical key/body/credential only; uncertainty requires reconciliation
Declared requirements
Before any paid call, refresh the live operation contract and POST the complete bounded budgeted plan to the separate API's /preflight. Unknown requirements block selection; compatible preflight is not permission to spend.