L1 ⚛ L1-187 ⊙ Testnet

Lattice Boltzmann Method (LBM) — mesoscale fluid

Fluid Dynamics · Lattice-Boltzmann BGK for incompressible flow

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⬇ L1-187.md

# ⚛ L1 Principle — Lattice Boltzmann Method (LBM) — mesoscale fluid **ID:** `L1-187` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Lattice-Boltzmann BGK for incompressible flow* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** distribution function lattice > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553977 --- ## 🧠 1. Introduction **Lattice Boltzmann Method (LBM) — mesoscale fluid** is a **linear inverse problem** whose unknown lives in **distribution function lattice** space, within the **Lattice-Boltzmann BGK for incompressible flow** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **piv microfluidic** sensing mechanism. The forward operator applies, in order: L · stream operator; L · collide bgk operator; L · moment extract 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** → L · stream → L · collide bgk → L · moment extract → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.moment_extract` `L.collide_bgk` `L.stream` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.stream` | L · stream operator | | `L.collide_bgk` | L · collide bgk operator | | `L.moment_extract` | L · moment extract operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Lattice-Boltzmann BGK for incompressible flow | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | distribution_function_lattice | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 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:** `lbm` · **Forward operator:** `lbm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 64 | | Snr db | dB | 30 | | N times | — | 5000 | | Grid error | — | 0 | | Compressibility error | — | 0 | | Relaxation time error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 4096 | | W | px | 32 – 4096 | | Z | — | 8 – 1024 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | Grid error | — | 0.0 – 0.3 | | Compressibility error | — | 0.0 – 0.2 | | Relaxation time error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe163b1f5951dceee763a1ab6959e1d1d974f6acf2884de4c30b7ee47c8d4dbb7` - **Chain tx hash:** `0x8019ccb6911183a9c551934c3be33ef2a93ebb84fcf539c11f801710eefa79ef` - **Chain block:** `41553977` --- ## File Mapping This bundle consists of: `L1-187.md`, `L1-187.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-187.md` | Source of truth — edit this | Human or LLM | | `L1-187.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 `L1-187`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-187.md).
Regenerate L1-187.json so every field matches the Markdown.
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L2-187-001 Lattice Boltzmann Method (LBM) — mesoscale fluid Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-187",
  "chain_block": 41553977,
  "chain_hash": "0xe163b1f5951dceee763a1ab6959e1d1d974f6acf2884de4c30b7ee47c8d4dbb7",
  "chain_tx_hash": "0x8019ccb6911183a9c551934c3be33ef2a93ebb84fcf539c11f801710eefa79ef",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "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": 3.2,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.stream",
      "L.collide_bgk",
      "L.moment_extract",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "piv_microfluidic",
    "solution_space": "distribution_function_lattice",
    "sub_domain": "Lattice-Boltzmann BGK for incompressible flow",
    "title": "Lattice Boltzmann Method (LBM) \u2014 mesoscale fluid"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "lbm_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_times",
      "SNR_dB",
      "relaxation_time_error",
      "grid_error",
      "compressibility_error",
      "relaxation_time_error",
      "grid_error",
      "compressibility_error"
    ],
    "allowed_problem_classes": [
      "lbm"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "lbm_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_times": 5000,
        "SNR_dB": 30,
        "W": 256,
        "Z": 64,
        "compressibility_error": 0.0,
        "grid_error": 0.0,
        "relaxation_time_error": 0.0
      },
      "problem_class": "lbm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        4096
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        4096
      ],
      "Z": [
        8,
        1024
      ],
      "compressibility_error": [
        0.0,
        0.2
      ],
      "grid_error": [
        0.0,
        0.3
      ],
      "relaxation_time_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Lattice-Boltzmann BGK for incompressible flow",
  "title": "Lattice Boltzmann Method (LBM) \u2014 mesoscale fluid"
}

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