L1 ⚛ L1-183 ⊙ Testnet

Volume of Fluid (VOF) — multiphase interface tracking

Fluid Dynamics · Interface-capturing VOF for multiphase

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⬇ principle.md ⬇ principle.json

Fork L1-183

⬇ L1-183.md ⬇ L1-183.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-183 (Volume of Fluid (VOF) — multiphase interface tracking) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-183.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-183.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_t dt `L.surface_tension` `L.interface_recon` `L.vof_advect` x + n,    n ~ 𝒩(0, σ²)

world state x (interface phase field multiphase)

→

L · vof advect `L.vof_advect`

→

L · interface recon `L.interface_recon`

→

L · surface tension `L.surface_tension`

→

Temporal integration ∫_t dt

→

observation y (mechanical detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-183.md

# ⚛ L1 Principle — Volume of Fluid (VOF) — multiphase interface tracking **ID:** `L1-183` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Interface-capturing VOF for multiphase* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** interface phase field multiphase > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553967 --- ## 🧠 1. Introduction **Volume of Fluid (VOF) — multiphase interface tracking** is a **nonlinear inverse problem** whose unknown lives in **interface phase field multiphase** space, within the **Interface-capturing VOF for multiphase** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **high speed camera piv** sensing mechanism. The forward operator applies, in order: L · vof advect operator; L · interface recon operator; L · surface tension 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 · vof advect → L · interface recon → L · surface tension → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.surface_tension` `L.interface_recon` `L.vof_advect` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.vof_advect` | L · vof advect operator | | `L.interface_recon` | L · interface recon operator | | `L.surface_tension` | L · surface tension operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Interface-capturing VOF for multiphase | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | interface_phase_field_multiphase | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 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:** `vof` · **Forward operator:** `vof_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 30 | | N times | — | 2000 | | Coalescence artifact | — | 0 | | Surface tension error | — | 0 | | Interface thickness error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 8192 | | W | px | 32 – 8192 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | Coalescence artifact | — | 0.0 – 0.3 | | Surface tension error | — | 0.0 – 0.3 | | Interface thickness error | — | 0.0 – 0.3 | ## 🎯 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 = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x66bf83eb9e0ff26f593944304efb5bcb6f9abff828e9cf4ac0ae2637898db3e4` - **Chain tx hash:** `0xa2712548089f3def45933aaddedbd99031cacd5d7ce790fd2af7aed1227b1dd0` - **Chain block:** `41553967` --- ## File Mapping This bundle consists of: `L1-183.md`, `L1-183.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-183.md` | Source of truth — edit this | Human or LLM | | `L1-183.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 `L1-183`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-183-001 Volume of Fluid (VOF) — multiphase interface tracking Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-183",
  "chain_block": 41553967,
  "chain_hash": "0x66bf83eb9e0ff26f593944304efb5bcb6f9abff828e9cf4ac0ae2637898db3e4",
  "chain_tx_hash": "0xa2712548089f3def45933aaddedbd99031cacd5d7ce790fd2af7aed1227b1dd0",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "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": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.vof_advect",
      "L.interface_recon",
      "L.surface_tension",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "high_speed_camera_piv",
    "solution_space": "interface_phase_field_multiphase",
    "sub_domain": "Interface-capturing VOF for multiphase",
    "title": "Volume of Fluid (VOF) \u2014 multiphase interface tracking"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "vof_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_times",
      "SNR_dB",
      "interface_thickness_error",
      "surface_tension_error",
      "coalescence_artifact",
      "interface_thickness_error",
      "surface_tension_error",
      "coalescence_artifact"
    ],
    "allowed_problem_classes": [
      "vof"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "vof_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "N_times": 2000,
        "SNR_dB": 30,
        "W": 512,
        "coalescence_artifact": 0.0,
        "interface_thickness_error": 0.0,
        "surface_tension_error": 0.0
      },
      "problem_class": "vof"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        8192
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        8192
      ],
      "coalescence_artifact": [
        0.0,
        0.3
      ],
      "interface_thickness_error": [
        0.0,
        0.3
      ],
      "surface_tension_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Interface-capturing VOF for multiphase",
  "title": "Volume of Fluid (VOF) \u2014 multiphase interface tracking"
}

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