L1 ⚛ L1-171 ⊙ Testnet

Compressible Navier-Stokes — viscous shock/boundary-layer

Fluid Dynamics · Compressible NS with shocks

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-171.md

# ⚛ L1 Principle — Compressible Navier-Stokes — viscous shock/boundary-layer **ID:** `L1-171` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Compressible NS with shocks* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** rho u p T fields > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553965 --- ## 🧠 1. Introduction **Compressible Navier-Stokes — viscous shock/boundary-layer** is a **nonlinear inverse problem** whose unknown lives in **rho u p T fields** space, within the **Compressible NS with shocks** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **schlieren bos pitot** sensing mechanism. The forward operator applies, in order: mass-balance: ∂_t ρ + ∇·(ρv) = 0; momentum balance (Navier-Stokes / Euler); L · energy operator; L · eos 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 → L · eos → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.eos` `L.energy` ∂_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` | L · energy operator | | `L.eos` | L · eos operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Compressible NS with shocks | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | rho_u_p_T_fields | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.7 | ## 📡 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:** `compress_ns` · **Forward operator:** `compress_ns_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 128 | | M mach | — | 1.5 | | Snr db | dB | 30 | | N times | — | 1000 | | K error | — | 0 | | Bc error | — | 0 | | Mu error | — | 0 | | Eos error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 8192 | | W | px | 32 – 8192 | | Z | — | 16 – 2048 | | M mach | — | 0.01 – 30 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | K error | — | 0.0 – 0.2 | | Bc error | — | 0.0 – 0.3 | | Mu error | — | 0.0 – 0.2 | | Eos error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5146218f09a4f691f6e1b1f3043a6147309cec1fd0121f0f13a813fb51b28839` - **Chain tx hash:** `0x67464b7d32b58602d046baac662f4b672ee3c0599bee614550c22f5c6c913870` - **Chain block:** `41553965` --- ## File Mapping This bundle consists of: `L1-171.md`, `L1-171.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-171.md` | Source of truth — edit this | Human or LLM | | `L1-171.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 `L1-171`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-171.md).
Regenerate L1-171.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-171-001 Compressible Navier-Stokes — viscous shock/boundary-layer Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-171",
  "chain_block": 41553965,
  "chain_hash": "0x5146218f09a4f691f6e1b1f3043a6147309cec1fd0121f0f13a813fb51b28839",
  "chain_tx_hash": "0x67464b7d32b58602d046baac662f4b672ee3c0599bee614550c22f5c6c913870",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.continuity",
      "L.momentum",
      "L.energy",
      "L.eos",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "schlieren_bos_pitot",
    "solution_space": "rho_u_p_T_fields",
    "sub_domain": "Compressible NS with shocks",
    "title": "Compressible Navier-Stokes \u2014 viscous shock/boundary-layer"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "compress_ns_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_times",
      "M_mach",
      "SNR_dB",
      "mu_error",
      "k_error",
      "eos_error",
      "bc_error",
      "mu_error",
      "k_error",
      "eos_error",
      "bc_error"
    ],
    "allowed_problem_classes": [
      "compress_ns"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "compress_ns_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "M_mach": 1.5,
        "N_times": 1000,
        "SNR_dB": 30,
        "W": 512,
        "Z": 128,
        "bc_error": 0.0,
        "eos_error": 0.0,
        "k_error": 0.0,
        "mu_error": 0.0
      },
      "problem_class": "compress_ns"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        8192
      ],
      "M_mach": [
        0.01,
        30
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        8192
      ],
      "Z": [
        16,
        2048
      ],
      "bc_error": [
        0.0,
        0.3
      ],
      "eos_error": [
        0.0,
        0.1
      ],
      "k_error": [
        0.0,
        0.2
      ],
      "mu_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Compressible NS with shocks",
  "title": "Compressible Navier-Stokes \u2014 viscous shock/boundary-layer"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.