Precedence levels check

precedence-levels-check · version 1.0.0 · Numbers & math · free, no key needed

Check whether claimed node levels exactly equal the earliest levels induced by a caller-supplied DAG.

Use when you need to: check claimed earliest dependency levels · verify minimum-depth level partition · audit longest-predecessor ranks.

Decide before calling

Read the versioned contract and the supported scope below. Reuse precedence-levels-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use precedence-levels-check@1.0.0 for check claimed earliest dependency levels. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• check claimed earliest dependency levels
• verify minimum-depth level partition
• audit longest-predecessor ranks
• find first incorrect DAG level
• validate canonical precedence layers
• check earliest-start stage assignment

Not supported

• compute or repair a claimed result
• infer dependencies from prose
• accept cyclic dependency graphs

Behavior

• nodes and identifiers use exact Unicode scalar-value string equality; no normalization or trimming; null is never an identifier.
• nodes must be unique, every edge endpoint must be declared, self-edges and cyclic graphs are invalid_input.
• A well-typed claim is valid only if it contains every source node exactly once and satisfies the tool-specific precedence rule.
• Claims are never repaired; the first issue is reported by claim index, then source node order, then source edge order.
• Duplicate edges are allowed and have identical semantics to one edge.
• The exact level of a node is 0 for a source, otherwise one plus the maximum level of its immediate predecessors; groups and members retain caller order but every group is nonempty.
• Every output names reference_version Kahn-1962-topological-order-and-poset-linear-extension.

Input

• nodes (array of string, required): max items 5000; each min length 1; each max length 128
• edges (array of array of string, required): max items 20000; each min items 2; each max items 2; each each min length 1; each each max length 128
• levels (array of array of string, required): max items 5000; each min items 1; each max items 5000; each each min length 1; each each max length 128

Output

• valid (boolean, required)
• reason (string, optional)
• discrepancy (object, optional)
• reference_version (constant "Kahn-1962-topological-order-and-poset-linear-extension", required)

Limits

• max nodes: 5000
• max edges: 20000
• max id bytes: 128
• max input bytes: 1000000

Example

Request input:

{
  "nodes": [
    "a",
    "b",
    "c"
  ],
  "edges": [
    [
      "a",
      "c"
    ],
    [
      "b",
      "c"
    ]
  ],
  "levels": [
    [
      "b",
      "a"
    ],
    [
      "c"
    ]
  ]
}

Response:

{
  "result": {
    "valid": true,
    "reference_version": "Kahn-1962-topological-order-and-poset-linear-extension"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "precedence-levels-check",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "a",
      "b",
      "c"
    ],
    "edges": [
      [
        "a",
        "c"
      ],
      [
        "b",
        "c"
      ]
    ],
    "levels": [
      [
        "b",
        "a"
      ],
      [
        "c"
      ]
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/precedence-levels-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["a","b","c"],"edges":[["a","c"],["b","c"]],"levels":[["b","a"],["c"]]}'

The machine-readable contract is at /v1/tools/precedence-levels-check/versions/1.0.0.

CLI

node cli.mjs run precedence-levels-check 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Precedence order check: Check whether a claimed node order is exactly a precedence-respecting linear extension of a caller-supplied DAG.
• Precedence batches check: Check whether claimed parallel batches contain every node once and respect a caller-supplied DAG.
• Maxflow certificate check: Check an exact max-flow/min-cut certificate and return the first deterministic discrepancy.
• Network flow feasibility check: Check a claimed s-t flow for capacity bounds and conservation with exact integers; returns the first bad edge or node.
• Permutation ranked check: Check exact stable ordinal ranks for decimal-string values and nulls, reporting the first source-index discrepancy.
• Coloring validity check: Check an indexed graph coloring certificate and report the first uncovered vertex or monochromatic edge.