L1 ⚛ L1-175 ⊙ Testnet

Potential Flow — irrotational inviscid

Fluid Dynamics · Laplace equation for irrotational flow

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⬇ L1-175.md

# ⚛ L1 Principle — Potential Flow — irrotational inviscid **ID:** `L1-175` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Laplace equation for irrotational flow* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** velocity potential > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553965 --- ## 🧠 1. Introduction **Potential Flow — irrotational inviscid** is a **linear inverse problem** whose unknown lives in **velocity potential** space, within the **Laplace equation for irrotational flow** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **pressure aerodynamic** sensing mechanism. The forward operator applies, in order: L · laplace operator; L · source sink operator; L · boundary match operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · laplace → L · source sink → L · boundary match → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.boundary_match` `L.source_sink` `L.laplace` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.laplace` | L · laplace operator | | `L.source_sink` | L · source sink operator | | `L.boundary_match` | L · boundary match operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Laplace equation for irrotational flow | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | velocity_potential | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 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:** `potential` · **Forward operator:** `potential_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 30 | | Bc error | — | 0 | | Circulation error | — | 0 | | Compressibility correction error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Snr db | dB | 0 – 40 | | Bc error | — | 0.0 – 0.3 | | Circulation error | — | 0.0 – 0.2 | | Compressibility correction error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x99742ee6dc6c86cc7b60953792156b1f6a523a9efcfdf39f453990e501c50775` - **Chain tx hash:** `0x70ae47e3911a1eab4976801091c34b9f393151e2cd3257ab77d6e5dfafec894e` - **Chain block:** `41553965` --- ## File Mapping This bundle consists of: `L1-175.md`, `L1-175.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-175.md` | Source of truth — edit this | Human or LLM | | `L1-175.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 `L1-175`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-175.md).
Regenerate L1-175.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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L2-175-001 Potential Flow — irrotational inviscid Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-175",
  "chain_block": 41553965,
  "chain_hash": "0x99742ee6dc6c86cc7b60953792156b1f6a523a9efcfdf39f453990e501c50775",
  "chain_tx_hash": "0x70ae47e3911a1eab4976801091c34b9f393151e2cd3257ab77d6e5dfafec894e",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "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": 2.8,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.laplace",
      "L.source_sink",
      "L.boundary_match",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "pressure_aerodynamic",
    "solution_space": "velocity_potential",
    "sub_domain": "Laplace equation for irrotational flow",
    "title": "Potential Flow \u2014 irrotational inviscid"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "potential_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "SNR_dB",
      "circulation_error",
      "bc_error",
      "compressibility_correction_error",
      "circulation_error",
      "bc_error",
      "compressibility_correction_error"
    ],
    "allowed_problem_classes": [
      "potential"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "potential_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "SNR_dB": 30,
        "W": 256,
        "bc_error": 0.0,
        "circulation_error": 0.0,
        "compressibility_correction_error": 0.0
      },
      "problem_class": "potential"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        2048
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "bc_error": [
        0.0,
        0.3
      ],
      "circulation_error": [
        0.0,
        0.2
      ],
      "compressibility_correction_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Laplace equation for irrotational flow",
  "title": "Potential Flow \u2014 irrotational inviscid"
}

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