# Halowerk Simple Graph Complete Maximal Clique Family Verifier

> Halowerk Simple Graph Complete Maximal Clique Family Verifier is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Verifies that a submitted family of cliques constitutes the complete set of maximal cliques for a given simple graph, ensuring all overlapping all-to-all subgroups are accounted for.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-REST-B15/simple-graph-complete-maximal-clique-family?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/halowerk-simple-graph-complete-maximal-clique-family-verifier-9e2b2626
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_wPg2QOEDD6--5HZPZpXCv

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability halowerk-simple-graph-complete-maximal-clique-family-verifier-9e2b2626 -d '<json body>'
```

Example prompt: Can you check whether the clique family I've listed covers all maximal cliques for my 5-node graph with edges [[0,1],[1,2],[2,3],[3,4],[0,4],[1,3]]? Here's the claimed clique set I want verified.

## When to prefer this

Choose this endpoint when you need to formally verify the completeness of a maximal clique enumeration on a small simple graph (up to 10 nodes, 100 edges) rather than computing cliques from scratch. It is ideal for validating algorithm outputs, auditing stored clique families, or confirming that community detection results are exhaustive.

## Known failure modes

- Graph too large (n > 10 nodes) returns a validation error
- Edge list exceeds 100 edges, triggering a schema rejection
- Node indices in edges exceed n-1, causing an invalid graph error
- Malformed clique claim structure returns a 400 bad request
- Claimed cliques contain non-existent edges, resulting in a verification failure response

## How this service works

Verify the full vertex family of maximal cliques so overlapping all-to-all groups retain their identities.

## Output

The endpoint returns a verification result indicating whether the submitted clique family is exactly the complete set of maximal cliques for the given graph, flagging any missing or spurious cliques and confirming that all overlapping all-to-all subgroups retain their identities.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "cliques"
   ],
   "properties": {
    "cliques": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "n",
        "edges"
       ],
       "properties": {
        "n": {
         "type": "integer",
         "maximum": 10,
         "minimum": 1
        },
        "edges": {
         "type": "array",
         "items": {
          "type": "array",
          "items": {
           "type": "integer",
           "maximum": 12,
           "minimum": 0
          },
          "maxItems": 2,
          "minItems": 2
         },
         "maxItems": 100,
         "minItems": 0
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/halowerk-simple-graph-complete-maximal-clique-family-verifier-9e2b2626/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)