# Inextensible Catenary Inverse Endpoint Slack Shape & Tension Solver

> Inextensible Catenary Inverse Endpoint Slack Shape & Tension Solver 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).

Given geometric and physical parameters of a slack cable, recovers the anonymous catenary model and computes its local geometric shape and tension state at sampled horizontal positions.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/inextensible-catenary-inverse-endpoint-slack-shape-tension?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/inextensible-catenary-inverse-endpoint-slack-shape-tension-solver-126f7dcb
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_dt74rxKfsilt2v_YurrNR

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 inextensible-catenary-inverse-endpoint-slack-shape-tension-solver-126f7dcb -d '<json body>'
```

Example prompt: I have a slack cable spanning 80 meters horizontally with a 3-meter vertical offset between supports, total cable length of 83.5 meters, and a weight per unit length of 12.5 N/m — can you recover the catenary model and compute the local shape and tension at horizontal positions 0, 20, 40, 60, and 80 meters?

## When to prefer this

Choose this endpoint when you need to solve the inverse catenary problem — recovering the cable model and local physics from geometric and physical cable parameters — rather than a forward simulation. It is specifically suited for inextensible cable models (no elastic stretch), making it appropriate for heavy structural cables, transmission lines, and rigging where material extension is negligible. Prefer this over general numerical ODE solvers when you need fast, closed-form catenary results with per-point tension output.

## Known failure modes

- Cable length shorter than horizontal span — physically impossible, returns validation error
- Horizontal samples outside the [0, horizontal_span] range may produce extrapolated or error responses
- Extreme weight-per-length or span values near schema limits may cause numerical instability
- Missing required fields (horizontal_span, cable_length, etc.) return schema validation errors
- Claim field mismatch or invalid artifact structure returns a 400-level error

## How this service works

Recover an anonymous slack cable model and its local geometric/tension state.

## Output

Returns the recovered anonymous catenary model (including catenary constant and reference parameters) together with per-sample local geometric state (position, slope, curvature) and tension values at each requested horizontal sample position along the cable.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "catenary"
   ],
   "properties": {
    "catenary": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "horizontal_span",
        "vertical_offset",
        "cable_length",
        "weight_per_length",
        "horizontal_samples"
       ],
       "properties": {
        "cable_length": {
         "type": "number",
         "maximum": 100000,
         "minimum": 0.001
        },
        "horizontal_span": {
         "type": "number",
         "maximum": 10000,
         "minimum": 0.001
        },
        "vertical_offset": {
         "type": "number",
         "maximum": 10000,
         "minimum": -10000
        },
        "weight_per_length": {
         "type": "number",
         "maximum": 1000000,
         "minimum": 0.000001
        },
        "horizontal_samples": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 10000,
          "minimum": 0
         },
         "maxItems": 32,
         "minItems": 1
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/inextensible-catenary-inverse-endpoint-slack-shape-tension-solver-126f7dcb/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)