L1 ⚛ L1-173 ⊙ Testnet

Stokes Flow — low-Re linear viscous

Fluid Dynamics · Creeping Stokes flow (Re<<1)

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⬇ L1-173.md

# ⚛ L1 Principle — Stokes Flow — low-Re linear viscous **ID:** `L1-173` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Creeping Stokes flow (Re<<1)* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D stokes velocity > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553965 --- ## 🧠 1. Introduction **Stokes Flow — low-Re linear viscous** is a **linear inverse problem** whose unknown lives in **3D stokes velocity** space, within the **Creeping Stokes flow (Re<<1)** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **microscope piv** sensing mechanism. The forward operator applies, in order: L · momentum linear operator; mass-balance: ∂_t ρ + ∇·(ρv) = 0; L · pressure 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 · momentum linear → Continuity equation → L · pressure → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.pressure` ∂_t ρ + ∇·(ρv) `L.momentum_linear` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.momentum_linear` | L · momentum linear operator | | `L.continuity` | Mass-balance: ∂_t ρ + ∇·(ρv) = 0 | | `L.pressure` | L · pressure operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Creeping Stokes flow (Re<<1) | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | 3D_stokes_velocity | | 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:** `stokes` · **Forward operator:** `stokes_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 | | Snr db | dB | 30 | | Bc error | — | 0 | | Mu error | — | 0 | | Slip length error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 8 – 512 | | Snr db | dB | 0 – 40 | | Bc error | — | 0.0 – 0.2 | | Mu error | — | 0.0 – 0.1 | | Slip length error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc71bea2570e05b7e7947175c73b7d0dbd8f55fee5722bacdb4db89294609a772` - **Chain tx hash:** `0xc52e8a71499696ab7d559b423bde412d7805381b4dc2619c221aaeaf1063631e` - **Chain block:** `41553965` --- ## File Mapping This bundle consists of: `L1-173.md`, `L1-173.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-173.md` | Source of truth — edit this | Human or LLM | | `L1-173.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 `L1-173`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-173.md).
Regenerate L1-173.json so every field matches the Markdown.
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L2-173-001 Stokes Flow — low-Re linear viscous Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-173",
  "chain_block": 41553965,
  "chain_hash": "0xc71bea2570e05b7e7947175c73b7d0dbd8f55fee5722bacdb4db89294609a772",
  "chain_tx_hash": "0xc52e8a71499696ab7d559b423bde412d7805381b4dc2619c221aaeaf1063631e",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    }
  ],
  "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.momentum_linear",
      "L.continuity",
      "L.pressure",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "microscope_piv",
    "solution_space": "3D_stokes_velocity",
    "sub_domain": "Creeping Stokes flow (Re\u003c\u003c1)",
    "title": "Stokes Flow \u2014 low-Re linear viscous"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "stokes_forward"
    ],
    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "SNR_dB",
      "mu_error",
      "bc_error",
      "slip_length_error",
      "mu_error",
      "bc_error",
      "slip_length_error"
    ],
    "allowed_problem_classes": [
      "stokes"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0",
      "forward_operator": "stokes_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "SNR_dB": 30,
        "W": 128,
        "Z": 32,
        "bc_error": 0.0,
        "mu_error": 0.0,
        "slip_length_error": 0.0
      },
      "problem_class": "stokes"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        8,
        512
      ],
      "bc_error": [
        0.0,
        0.2
      ],
      "mu_error": [
        0.0,
        0.1
      ],
      "slip_length_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Creeping Stokes flow (Re\u003c\u003c1)",
  "title": "Stokes Flow \u2014 low-Re linear viscous"
}

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