L1 ⚛ L1-186 ⊙ Testnet

SPH — smoothed particle hydrodynamics

Fluid Dynamics · Lagrangian meshfree SPH

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⬇ L1-186.md

# ⚛ L1 Principle — SPH — smoothed particle hydrodynamics **ID:** `L1-186` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Lagrangian meshfree SPH* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** particle field meshfree > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553967 --- ## 🧠 1. Introduction **SPH — smoothed particle hydrodynamics** is a **nonlinear inverse problem** whose unknown lives in **particle field meshfree** space, within the **Lagrangian meshfree SPH** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **wave tank** sensing mechanism. The forward operator applies, in order: L · kernel approx operator; momentum balance (Navier-Stokes / Euler); L · density 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 · kernel approx → Momentum equation → L · density → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.density` ∂_t(ρv) + ∇·(ρv⊗v) `L.kernel_approx` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.kernel_approx` | L · kernel approx operator | | `L.momentum` | Momentum balance (navier-stokes / euler) | | `L.density` | L · density operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Lagrangian meshfree SPH | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | particle_field_meshfree | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `sph` · **Forward operator:** `sph_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N times | — | 2000 | | N particles | — | 1e+06 | | Boundary error | — | 0 | | Pressure instability | — | 0 | | Kernel bandwidth error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | N particles | — | 1000.0 – 10000000000.0 | | Boundary error | — | 0.0 – 0.3 | | Pressure instability | — | 0.0 – 0.3 | | Kernel bandwidth error | — | 0.0 – 0.3 | ## 🎯 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 = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xde64bb22e0d6ef12d032f705fcffe61267d305e8d2ac054a851a5abe012e90cc` - **Chain tx hash:** `0x6e3ec68a0dbeeec427d8fe4a9dd6f7203f050f360b9c10e1225839e7c9657caf` - **Chain block:** `41553967` --- ## File Mapping This bundle consists of: `L1-186.md`, `L1-186.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-186.md` | Source of truth — edit this | Human or LLM | | `L1-186.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 `L1-186`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-186.md).
Regenerate L1-186.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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L2-186-001 SPH — smoothed particle hydrodynamics Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553967,
  "chain_hash": "0xde64bb22e0d6ef12d032f705fcffe61267d305e8d2ac054a851a5abe012e90cc",
  "chain_tx_hash": "0x6e3ec68a0dbeeec427d8fe4a9dd6f7203f050f360b9c10e1225839e7c9657caf",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "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": 3.3,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.kernel_approx",
      "L.momentum",
      "L.density",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "wave_tank",
    "solution_space": "particle_field_meshfree",
    "sub_domain": "Lagrangian meshfree SPH",
    "title": "SPH \u2014 smoothed particle hydrodynamics"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
      "N_particles",
      "N_times",
      "SNR_dB",
      "kernel_bandwidth_error",
      "pressure_instability",
      "boundary_error",
      "kernel_bandwidth_error",
      "pressure_instability",
      "boundary_error"
    ],
    "allowed_problem_classes": [
      "sph"
    ],
    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
        "N_particles": 1000000.0,
        "N_times": 2000,
        "SNR_dB": 30,
        "boundary_error": 0.0,
        "kernel_bandwidth_error": 0.0,
        "pressure_instability": 0.0
      },
      "problem_class": "sph"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_particles": [
        1000.0,
        10000000000.0
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "boundary_error": [
        0.0,
        0.3
      ],
      "kernel_bandwidth_error": [
        0.0,
        0.3
      ],
      "pressure_instability": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Lagrangian meshfree SPH",
  "title": "SPH \u2014 smoothed particle hydrodynamics"
}

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