# Ideal Gas Euler-Riemann Complete Shock-Rarefaction-Contact State Solver

> Ideal Gas Euler-Riemann Complete Shock-Rarefaction-Contact State 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).

Solves the complete Euler-Riemann problem for a compressible ideal gas discontinuity, recovering all wave structures (shocks, rarefactions, contact discontinuities) and sampled conservative states at specified similarity coordinates.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B010/ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state?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/ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state-solver-06446e6f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_GF95gc0hPVqMhMJvQcxb9

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 ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state-solver-06446e6f -d '<json body>'
```

Example prompt: Solve the exact Euler-Riemann problem for an ideal gas with gamma=1.4, left state density=1.0 velocity=0.0 pressure=1.0, right state density=0.125 velocity=0.0 pressure=0.1 (classic Sod tube), and sample the complete conservative state solution at similarity coordinates -2.0, -0.5, 0.0, 0.5, 1.75, and 3.0.

## When to prefer this

Use this endpoint when you need the mathematically exact solution to the 1D Euler Riemann problem for an ideal gas — not an approximate or linearized Riemann solver. Ideal for validating CFD codes, generating reference solutions for shock tube problems, computing numerical fluxes exactly, or studying wave interaction structure. Prefer this over approximate Riemann solvers (Roe, HLLC, etc.) when exact wave speeds and intermediate states are needed. Only supports ideal (calorically perfect) gas with constant gamma; not suitable for real-gas equations of state.

## Known failure modes

- Left or right state density or pressure outside allowed range (0.000001–10000 / 0.000001–1000000) → validation error
- Gamma outside range [1.01, 2.0] → rejected input
- More than 32 similarity coordinates provided → schema violation
- Vacuum formation (opposing rarefactions that deplete pressure to zero) → may return error or degenerate state
- Similarity coordinates outside [-100000, 100000] → rejected
- Missing required left/right state fields → 400-level error

## How this service works

Recover all waves and sampled conservative states of an explicit compressible gas discontinuity.

## Output

Returns all wave speeds and types (shock, rarefaction head/tail, contact discontinuity), the intermediate star-region pressure and velocity, and the full conservative state (density, momentum, energy) sampled at each requested similarity coordinate (x/t value) across the Riemann fan.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "eulerRiemann"
   ],
   "properties": {
    "eulerRiemann": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "left",
        "right",
        "gamma",
        "similarity_coordinates"
       ],
       "properties": {
        "left": {
         "type": "object",
         "required": [
          "density",
          "velocity",
          "pressure"
         ],
         "properties": {
          "density": {
           "type": "number",
           "maximum": 10000,
           "minimum": 0.000001
          },
          "pressure": {
           "type": "number",
           "maximum": 1000000,
           "minimum": 0.000001
          },
          "velocity": {
           "type": "number",
           "maximum": 10000,
           "minimum": -10000
          }
         },
         "additionalProperties": false
        },
        "gamma": {
         "type": "number",
         "maximum": 2,
         "minimum": 1.01
        },
        "right": {
         "type": "object",
         "required": [
          "density",
          "velocity",
          "pressure"
         ],
         "properties": {
          "density": {
           "type": "number",
           "maximum": 10000,
           "minimum": 0.000001
          },
          "pressure": {
           "type": "number",
           "maximum": 1000000,
           "minimum": 0.000001
          },
          "velocity": {
           "type": "number",
           "maximum": 10000,
           "minimum": -10000
          }
         },
         "additionalProperties": false
        },
        "similarity_coordinates": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 100000,
          "minimum": -100000
         },
         "maxItems": 32,
         "minItems": 1
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/ideal-gas-euler-riemann-complete-shock-rarefaction-contact-state-solver-06446e6f/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)