Flow value check

flow-value-check · version 1.0.0 · Numbers & math · free, no key needed

Check a feasible exact integer flow and its claimed source value, returning the first discrepancy.

Use when you need to: check claimed flow value · validate network flow value · compare flow against claimed value.

Decide before calling

Read the versioned contract and the supported scope below. Reuse flow-value-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 flow-value-check@1.0.0 for check claimed flow value. 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 flow value
• validate network flow value
• compare flow against claimed value
• check source net outflow
• verify exact integer flow total
• find first flow value discrepancy

Not supported

• compute a maximum flow
• infer or repair missing edge flows

Behavior

• Feasibility is checked first in edge then node order; the value claim is checked only after feasibility succeeds.
• Flow value is total source outflow minus total source inflow, including parallel and antiparallel edges.
• Capacities and edge flows are canonical nonnegative decimal strings; claimed_value is a canonical signed decimal string. Arithmetic is exact.
• A false claim is reported and never replaced or silently repaired.
• 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 79; pattern ^(0|-?[1-9][0-9]*)$

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": "5"
    }
  ],
  "source": "s",
  "sink": "t",
  "flow": [
    "4"
  ],
  "claimed_value": "4"
}

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": "flow-value-check",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "s",
      "t"
    ],
    "edges": [
      {
        "from": "s",
        "to": "t",
        "capacity": "5"
      }
    ],
    "source": "s",
    "sink": "t",
    "flow": [
      "4"
    ],
    "claimed_value": "4"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/flow-value-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["s","t"],"edges":[{"from":"s","to":"t","capacity":"5"}],"source":"s","sink":"t","flow":["4"],"claimed_value":"4"}'

The machine-readable contract is at /v1/tools/flow-value-check/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• 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.
• Flow feasibility check: Check exact integer edge capacities and flow conservation, returning the first discrepancy.
• Maxflow certificate check: Check an exact max-flow/min-cut certificate and return the first deterministic discrepancy.
• Maximum flow certificate check: Check a claimed max flow with a min-cut certificate or residual search; reports the first failure or augmenting path.
• Permutation values check: Check whether claimed values are a SameValueZero multiset permutation, reporting the first source-order discrepancy.
• Stable sort result check: Check that a claimed record result is the exact ascending stable sort of the supplied source records.