L1 ⚛ L1-174 ⊙ Testnet

Boundary Layer — Prandtl / Blasius near-wall flow

Fluid Dynamics · Laminar and turbulent boundary layers

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Markdown — human-readable source of truth

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⬇ L1-174.md

# ⚛ L1 Principle — Boundary Layer — Prandtl / Blasius near-wall flow **ID:** `L1-174` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Laminar and turbulent boundary layers* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** velocity profile near wall > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553965 --- ## 🧠 1. Introduction **Boundary Layer — Prandtl / Blasius near-wall flow** is a **nonlinear inverse problem** whose unknown lives in **velocity profile near wall** space, within the **Laminar and turbulent boundary layers** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **hot wire piv** sensing mechanism. The forward operator applies, in order: L · prandtl bl operator; L · similarity operator; L · transition 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 · prandtl bl → L · similarity → L · transition → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.transition` `L.similarity` `L.prandtl_bl` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.prandtl_bl` | L · prandtl bl operator | | `L.similarity` | L · similarity operator | | `L.transition` | L · transition operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Laminar and turbulent boundary layers | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | velocity_profile_near_wall | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 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:** `boundary_layer` · **Forward operator:** `boundary_layer_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N y | — | 200 | | Re x | — | 1e+06 | | Snr db | dB | 30 | | Re x error | — | 0 | | Roughness error | — | 0 | | Pressure gradient error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N y | — | 32 – 10000 | | Re x | — | 100.0 – 10000000000.0 | | Snr db | dB | 0 – 40 | | Re x error | — | 0.0 – 0.1 | | Roughness error | — | 0.0 – 0.3 | | Pressure gradient error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc86fdd1107c12722f81c4dfed9f473281486663a91a1ed9c2eeec4bd6b6ecae6` - **Chain tx hash:** `0xeed16d987b690f4f718857ade27f039ed01e7d3a6aaedc1be4f7b610057a94f0` - **Chain block:** `41553965` --- ## File Mapping This bundle consists of: `L1-174.md`, `L1-174.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-174.md` | Source of truth — edit this | Human or LLM | | `L1-174.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 `L1-174`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-174.md).
Regenerate L1-174.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.

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L2-174-001 Boundary Layer — Prandtl / Blasius near-wall flow Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-174",
  "chain_block": 41553965,
  "chain_hash": "0xc86fdd1107c12722f81c4dfed9f473281486663a91a1ed9c2eeec4bd6b6ecae6",
  "chain_tx_hash": "0xeed16d987b690f4f718857ade27f039ed01e7d3a6aaedc1be4f7b610057a94f0",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 300,
    "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": 3.0,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.prandtl_bl",
      "L.similarity",
      "L.transition",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "hot_wire_piv",
    "solution_space": "velocity_profile_near_wall",
    "sub_domain": "Laminar and turbulent boundary layers",
    "title": "Boundary Layer \u2014 Prandtl / Blasius near-wall flow"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "boundary_layer_forward"
    ],
    "allowed_omega_dimensions": [
      "N_y",
      "Re_x",
      "SNR_dB",
      "Re_x_error",
      "pressure_gradient_error",
      "roughness_error",
      "Re_x_error",
      "pressure_gradient_error",
      "roughness_error"
    ],
    "allowed_problem_classes": [
      "boundary_layer"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "boundary_layer_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_y": 200,
        "Re_x": 1000000.0,
        "Re_x_error": 0.0,
        "SNR_dB": 30,
        "pressure_gradient_error": 0.0,
        "roughness_error": 0.0
      },
      "problem_class": "boundary_layer"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_y": [
        32,
        10000
      ],
      "Re_x": [
        100.0,
        10000000000.0
      ],
      "Re_x_error": [
        0.0,
        0.1
      ],
      "SNR_dB": [
        0,
        40
      ],
      "pressure_gradient_error": [
        0.0,
        0.3
      ],
      "roughness_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Laminar and turbulent boundary layers",
  "title": "Boundary Layer \u2014 Prandtl / Blasius near-wall flow"
}

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