Maxflow certificate check

maxflow-certificate-check · version 1.0.0 · Numbers & math · free, no key needed

Check an exact max-flow/min-cut certificate and return the first deterministic discrepancy.

Use when you need to: check max flow certificate · validate max flow min cut proof · check claimed maximum flow.

Decide before calling

Read the versioned contract and the supported scope below. Reuse maxflow-certificate-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 maxflow-certificate-check@1.0.0 for check max flow certificate. 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 max flow certificate
• validate max flow min cut proof
• check claimed maximum flow
• verify minimum cut witness
• audit flow optimality certificate
• find first maxflow certificate discrepancy

Not supported

• compute a maximum flow
• choose or repair a cut partition

Behavior

• The claimed flow is checked for feasibility first, then source value, then source-side membership, cut capacity, and crossing-edge equality conditions.
• source_side is an unordered duplicate-free list naming the cut side containing source and excluding sink; omitted nodes are on the sink side.
• Cut capacity sums original capacities of edges directed from source_side to its complement; parallel edges count separately.
• All numeric fields are canonical nonnegative decimal strings and arithmetic is exact.
• By max-flow/min-cut equality, a feasible flow whose value equals this cut capacity is maximum and the cut is minimum.
• Reference version: Ford-Fulkerson max-flow/min-cut theorem (Ahuja-Magnanti-Orlin 1993, Sections 6.1-6.5).

Input

• nodes (array of string, required): min items 2; max items 256; each min length 1; each max length 64
• edges (array of object, required): max items 4096
• source (string, required): min length 1; max length 64
• sink (string, required): min length 1; max length 64
• flow (array of string, required): max items 4096; each min length 1; each max length 78; each pattern ^(0|[1-9][0-9]*)$
• claimed_value (string, required): min length 1; max length 78; pattern ^(0|[1-9][0-9]*)$
• source_side (array of string, required): min items 1; max items 256; each min length 1; each max length 64

Output

• valid (boolean, required)
• reason (string or null, required)
• discrepancy (null or object, required)
• reference_version (constant "Ford-Fulkerson max-flow/min-cut theorem (Ahuja-Magnanti-Orlin 1993, Sections 6.1-6.5)", required)

Limits

• max nodes: 256
• max edges: 4096
• max integer digits: 78
• max node id bytes: 64

Example

Request input:

{
  "nodes": [
    "s",
    "t"
  ],
  "edges": [
    {
      "from": "s",
      "to": "t",
      "capacity": "3"
    }
  ],
  "source": "s",
  "sink": "t",
  "flow": [
    "3"
  ],
  "claimed_value": "3",
  "source_side": [
    "s"
  ]
}

Response:

{
  "result": {
    "valid": true,
    "reason": null,
    "discrepancy": null,
    "reference_version": "Ford-Fulkerson max-flow/min-cut theorem (Ahuja-Magnanti-Orlin 1993, Sections 6.1-6.5)"
  }
}

How to call it

MCP

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

{
  "id": "maxflow-certificate-check",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "s",
      "t"
    ],
    "edges": [
      {
        "from": "s",
        "to": "t",
        "capacity": "3"
      }
    ],
    "source": "s",
    "sink": "t",
    "flow": [
      "3"
    ],
    "claimed_value": "3",
    "source_side": [
      "s"
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/maxflow-certificate-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["s","t"],"edges":[{"from":"s","to":"t","capacity":"3"}],"source":"s","sink":"t","flow":["3"],"claimed_value":"3","source_side":["s"]}'

The machine-readable contract is at /v1/tools/maxflow-certificate-check/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• Maximum flow certificate check: Check a claimed max flow with a min-cut certificate or residual search; reports the first failure or augmenting path.
• Network cut capacity check: Check a claimed s-t cut: source-side membership, the edges crossing it and its capacity, with exact integers.
• Bipartite coloring check: Check a complete 0/1 coloring witness for graph bipartiteness and report the first certificate discrepancy.
• Flow value check: Check a feasible exact integer flow and its claimed source value, returning the first discrepancy.
• Join inner result check: Check a claimed ordered inner join index result and report its first discrepancy.
• Join left result check: Check a claimed ordered left join index result and report its first discrepancy.