# Schwarzschild Null-Scattering Ray Bending Coordinate Time Field Ledger

> Schwarzschild Null-Scattering Ray Bending Coordinate Time Field Ledger 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).

Computes relativistic light-scattering (ray bending) artifacts in Schwarzschild spacetime geometry, returning a complete bounded null-geodesic coordinate-time field ledger for given mass, periapsis, and radial sample points.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B012/schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger?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/schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger-af6bb8ed
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_0aVGLGvVJyy-Vp4jf_bwq

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 schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger-af6bb8ed -d '<json body>'
```

Example prompt: Calculate the full null-geodesic ray bending coordinate-time ledger for a Schwarzschild black hole with mass parameter 1.5, periapsis radius 0.5, sampled at radii [0.5, 1.0, 2.5, 5.0, 10.0].

## When to prefer this

Choose this endpoint when you need precise, general-relativistic null-geodesic ray bending computations in Schwarzschild spacetime — particularly for gravitational lensing studies, black hole shadow modeling, or photon orbit analysis. It is well-suited for research or simulation workflows that require coordinate-time field data at multiple radii for a specified mass and periapsis. Prefer this over Newtonian or approximate deflection-angle calculators when full GR accuracy and a structured ledger output are required.

## Known failure modes

- Invalid mass_parameter outside [0.01, 10] returns validation error
- periapsis_radius below 0.0301 (inside photon sphere) may cause unphysical results or error
- sample_radii values below periapsis_radius may be rejected as unphysical
- Exceeding 24 sample radii returns a schema validation error
- Missing required fields (mass_parameter, periapsis_radius, sample_radii) returns 400 Bad Request
- Payment not provided or insufficient USDC balance returns 402 Payment Required

## How this service works

Recover a complete bounded relativistic light-scattering artifact from an explicit spherical spacetime model.

## Output

Returns a complete bounded relativistic light-scattering artifact record: a coordinate-time field ledger capturing the null-geodesic ray bending trajectory through Schwarzschild spacetime, computed at each specified sample radius given the mass parameter and periapsis. The response includes the structured artifact with scattering data points and associated metadata.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "schwarzschild"
   ],
   "properties": {
    "schwarzschild": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "mass_parameter",
        "periapsis_radius",
        "sample_radii"
       ],
       "properties": {
        "sample_radii": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 20000,
          "minimum": 0.0301
         },
         "maxItems": 24,
         "minItems": 1
        },
        "mass_parameter": {
         "type": "number",
         "maximum": 10,
         "minimum": 0.01
        },
        "periapsis_radius": {
         "type": "number",
         "maximum": 1000,
         "minimum": 0.0301
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger-af6bb8ed/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)