# Abelian Sandpile Sink Stabilization & Odometer

> Abelian Sandpile Sink Stabilization & Odometer 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).

Stabilizes an abelian sandpile model on a finite graph with a designated sink, returning the unique stable chip configuration, per-vertex toppling counts (odometer), and chips absorbed by the sink.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-NIGHT-ECMA/abelian-sandpile-sink-stabilization-odometer?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/abelian-sandpile-sink-stabilization-odometer-4eac2a26
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_nv8_fZ5OdiLxnVR12XoIX

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 abelian-sandpile-sink-stabilization-odometer-4eac2a26 -d '<json body>'
```

Example prompt: Stabilize this abelian sandpile: 4 vertices, sink at vertex 0, adjacency matrix [[0,2,1,0],[2,0,1,0],[1,1,0,2],[0,0,2,0]], starting chips [0,3,5,2], and my claimed odometer is [0,1,2,1]. Give me the unique stable configuration, per-vertex toppling counts, and how many chips the sink absorbed.

## When to prefer this

Use this endpoint when you need an authoritative, offline-capable computation of abelian sandpile stabilization on small finite graphs (up to 16 vertices) including the odometer function and sink absorption count. Prefer it over manual simulation when you need to verify a proposed odometer/claim, need deterministic results for testing chip-firing algorithms, or require all three outputs (stable config, toppling counts, sink chips) simultaneously.

## Known failure modes

- Adjacency matrix dimensions inconsistent with chips/claim arrays — returns validation error
- Sink index out of range (>15 or negative) — rejected by schema
- Chip values exceeding 256 or odometer values exceeding 2048 — schema rejection
- Graph not connected or no path to sink — may result in non-termination or error
- Adjacency matrix not symmetric (directed graph) — may produce unexpected results
- Claim array length mismatch with adjacency matrix size — returns error

## How this service works

An offline chip-firing model test agent needs the unique stabilized configuration, per-vertex toppling counts and chips absorbed by a sink. Not checking arbitrary Petri boundedness or a supplied transition trace.

## Output

Returns the unique stable chip configuration (array of non-negative integers per vertex), the odometer (array of toppling counts per vertex), and the total number of chips absorbed by the designated sink vertex during stabilization.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "sandpile"
   ],
   "properties": {
    "sandpile": {
     "type": "object",
     "required": [
      "adjacency",
      "sink",
      "chips",
      "claim"
     ],
     "properties": {
      "sink": {
       "type": "integer",
       "maximum": 15,
       "minimum": 0
      },
      "chips": {
       "type": "array",
       "items": {
        "type": "integer",
        "maximum": 256,
        "minimum": 0
       },
       "maxItems": 16,
       "minItems": 2
      },
      "claim": {
       "type": "array",
       "items": {
        "type": "integer",
        "maximum": 2048,
        "minimum": 0
       },
       "maxItems": 16,
       "minItems": 2
      },
      "adjacency": {
       "type": "array",
       "items": {
        "type": "array",
        "items": {
         "type": "integer",
         "maximum": 8,
         "minimum": 0
        },
        "maxItems": 16,
        "minItems": 2
       },
       "maxItems": 16,
       "minItems": 2
      }
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/abelian-sandpile-sink-stabilization-odometer-4eac2a26/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)