L1 ⚛ L1-193 ⊙ Testnet

Stefan Problem — fluid-side melt-front tracking

Fluid Dynamics · Phase-change with fluid convection

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⬇ L1-193.md

# ⚛ L1 Principle — Stefan Problem — fluid-side melt-front tracking **ID:** `L1-193` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Phase-change with fluid convection* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** moving interface and flow > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553978 --- ## 🧠 1. Introduction **Stefan Problem — fluid-side melt-front tracking** is a **nonlinear inverse problem** whose unknown lives in **moving interface and flow** space, within the **Phase-change with fluid convection** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **thermocouples piv** sensing mechanism. The forward operator applies, in order: L · heat transport operator; L · convect operator; L · stefan condition 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 · heat transport → L · convect → L · stefan condition → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.stefan_condition` `L.convect` `L.heat_transport` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.heat_transport` | L · heat transport operator | | `L.convect` | L · convect operator | | `L.stefan_condition` | L · stefan condition operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Phase-change with fluid convection | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | moving_interface_and_flow | | 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:** `stefan_fluid` · **Forward operator:** `stefan_fluid_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Ra | — | 100000 | | Snr db | dB | 30 | | N times | — | 2000 | | K solid error | — | 0 | | K liquid error | — | 0 | | Latent heat error | — | 0 | | Natural convection error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Ra | — | 10 – 10000000000.0 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | K solid error | — | 0.0 – 0.2 | | K liquid error | — | 0.0 – 0.2 | | Latent heat error | — | 0.0 – 0.2 | | Natural convection 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:** `0x63fec170e5dc4e42c3e62ba3ff828715b18e7ba10ea77a8ffb8b20cde7d4c23d` - **Chain tx hash:** `0x9165dd882250d33c88c0c9ebda83a3876fa87a0afa6a3c51d04e8724a4c029d0` - **Chain block:** `41553978` --- ## File Mapping This bundle consists of: `L1-193.md`, `L1-193.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-193.md` | Source of truth — edit this | Human or LLM | | `L1-193.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 `L1-193`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-193.md).
Regenerate L1-193.json so every field matches the Markdown.
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L2-193-001 Stefan Problem — fluid-side melt-front tracking Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-193",
  "chain_block": 41553978,
  "chain_hash": "0x63fec170e5dc4e42c3e62ba3ff828715b18e7ba10ea77a8ffb8b20cde7d4c23d",
  "chain_tx_hash": "0x9165dd882250d33c88c0c9ebda83a3876fa87a0afa6a3c51d04e8724a4c029d0",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "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": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "L.convect",
      "L.stefan_condition",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "thermocouples_piv",
    "solution_space": "moving_interface_and_flow",
    "sub_domain": "Phase-change with fluid convection",
    "title": "Stefan Problem \u2014 fluid-side melt-front tracking"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "stefan_fluid_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_times",
      "Ra",
      "SNR_dB",
      "latent_heat_error",
      "k_liquid_error",
      "k_solid_error",
      "natural_convection_error",
      "latent_heat_error",
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      "k_solid_error",
      "natural_convection_error"
    ],
    "allowed_problem_classes": [
      "stefan_fluid"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "stefan_fluid_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_times": 2000,
        "Ra": 100000.0,
        "SNR_dB": 30,
        "W": 256,
        "k_liquid_error": 0.0,
        "k_solid_error": 0.0,
        "latent_heat_error": 0.0,
        "natural_convection_error": 0.0
      },
      "problem_class": "stefan_fluid"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        45.0
      ]
    },
    "omega_bounds": {
      "H": [
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        2048
      ],
      "N_times": [
        100,
        1000000
      ],
      "Ra": [
        10,
        10000000000.0
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "k_liquid_error": [
        0.0,
        0.2
      ],
      "k_solid_error": [
        0.0,
        0.2
      ],
      "latent_heat_error": [
        0.0,
        0.2
      ],
      "natural_convection_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Phase-change with fluid convection",
  "title": "Stefan Problem \u2014 fluid-side melt-front tracking"
}

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