L1 ⚛ L1-172 ⊙ Testnet

Euler Equations — inviscid compressible

Fluid Dynamics · Inviscid compressible Euler

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⬇ L1-172.md

# ⚛ L1 Principle — Euler Equations — inviscid compressible **ID:** `L1-172` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Inviscid compressible Euler* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** rho u p inviscid > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553965 --- ## 🧠 1. Introduction **Euler Equations — inviscid compressible** is a **nonlinear inverse problem** whose unknown lives in **rho u p inviscid** space, within the **Inviscid compressible Euler** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **pressure schlieren** sensing mechanism. The forward operator applies, in order: mass-balance: ∂_t ρ + ∇·(ρv) = 0; momentum balance (Navier-Stokes / Euler); L · energy inviscid operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → Continuity equation → Momentum equation → L · energy inviscid → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.energy_inviscid` ∂_t(ρv) + ∇·(ρv⊗v) ∂_t ρ + ∇·(ρv) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.continuity` | Mass-balance: ∂_t ρ + ∇·(ρv) = 0 | | `L.momentum` | Momentum balance (navier-stokes / euler) | | `L.energy_inviscid` | L · energy inviscid operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Inviscid compressible Euler | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | rho_u_p_inviscid | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `euler` · **Forward operator:** `euler_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 30 | | N times | — | 1000 | | Bc error | — | 0 | | Eos error | — | 0 | | Limiter error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 8192 | | W | px | 32 – 8192 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | Bc error | — | 0.0 – 0.3 | | Eos error | — | 0.0 – 0.1 | | Limiter error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 23.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4e1a0e49c247bd9c7e4a4974a740b9b12001664edc1f3cc9319bbf8b5ab0b5af` - **Chain tx hash:** `0xf79147acb1573641232236128b9cc8c2ba9f457d5e0b575bb9ff64b4c318f34a` - **Chain block:** `41553965` --- ## File Mapping This bundle consists of: `L1-172.md`, `L1-172.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-172.md` | Source of truth — edit this | Human or LLM | | `L1-172.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-172`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-172.md).
Regenerate L1-172.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-172-001 Euler Equations — inviscid compressible Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Fluid Dynamics",
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    "L_DAG": 3.3,
    "carrier": "mechanical",
    "difficulty_delta": 3,
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "pressure_schlieren",
    "solution_space": "rho_u_p_inviscid",
    "sub_domain": "Inviscid compressible Euler",
    "title": "Euler Equations \u2014 inviscid compressible"
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      "eos_error": [
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      ],
      "limiter_error": [
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        0.3
      ]
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Inviscid compressible Euler",
  "title": "Euler Equations \u2014 inviscid compressible"
}

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