L1 ⚛ L1-202 ⊙ Testnet

Phase Change Material — Stefan moving-boundary problem

Heat Transfer · Latent-heat tracking (melt/solid boundary)

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⬇ principle.md ⬇ principle.json

Fork L1-202

⬇ L1-202.md ⬇ L1-202.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-202 (Phase Change Material — Stefan moving-boundary problem) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-202.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-202.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.heat_transport` `L.interface_tracking` `L.enthalpy` x + n,    n ~ 𝒩(0, σ²)

world state x (moving interface and T fields)

→

L · enthalpy `L.enthalpy`

→

L · interface tracking `L.interface_tracking`

→

L · heat transport `L.heat_transport`

→

Temporal integration ∫_t dt

→

observation y (thermal detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-202.md

# ⚛ L1 Principle — Phase Change Material — Stefan moving-boundary problem **ID:** `L1-202` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *Latent-heat tracking (melt/solid boundary)* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** moving interface and T fields > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034 --- ## 🧠 1. Introduction **Phase Change Material — Stefan moving-boundary problem** is a **nonlinear inverse problem** whose unknown lives in **moving interface and T fields** space, within the **Latent-heat tracking (melt/solid boundary)** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **thermocouples xray** sensing mechanism. The forward operator applies, in order: L · enthalpy operator; L · interface tracking operator; L · heat transport 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 · enthalpy → L · interface tracking → L · heat transport → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.heat_transport` `L.interface_tracking` `L.enthalpy` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.enthalpy` | L · enthalpy operator | | `L.interface_tracking` | L · interface tracking operator | | `L.heat_transport` | L · heat transport operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | Latent-heat tracking (melt/solid boundary) | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | moving_interface_and_T_fields | | 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` · **Forward operator:** `stefan_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Snr db | dB | 30 | | N sensors | — | 16 | | K solid error | — | 0 | | K liquid error | — | 0 | | Supercool error | — | 0 | | Latent heat error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Snr db | dB | 0 – 40 | | N sensors | — | 4 – 256 | | K solid error | — | 0.0 – 0.1 | | K liquid error | — | 0.0 – 0.1 | | Supercool error | — | 0.0 – 5.0 | | Latent heat error | — | 0.0 – 0.1 | ## 🎯 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 = `700` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xef9180b73263bebaa1ae1c5c21b02b8607d77a0d415b6edb2e9645e477ec87ed` - **Chain tx hash:** `0x48784f517e1b75a75d7553fd9bcc549cd76ce6494694fe85e4e082a93e046253` - **Chain block:** `41554034` --- ## File Mapping This bundle consists of: `L1-202.md`, `L1-202.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-202.md` | Source of truth — edit this | Human or LLM | | `L1-202.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 `L1-202`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-202-001 Phase Change Material — Stefan moving-boundary problem Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-202",
  "chain_block": 41554034,
  "chain_hash": "0xef9180b73263bebaa1ae1c5c21b02b8607d77a0d415b6edb2e9645e477ec87ed",
  "chain_tx_hash": "0x48784f517e1b75a75d7553fd9bcc549cd76ce6494694fe85e4e082a93e046253",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 5,
    "kappa": 700,
    "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": "thermal",
    "difficulty_delta": 5,
    "domain": "Heat Transfer",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.enthalpy",
      "L.interface_tracking",
      "L.heat_transport",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "thermocouples_xray",
    "solution_space": "moving_interface_and_T_fields",
    "sub_domain": "Latent-heat tracking (melt/solid boundary)",
    "title": "Phase Change Material \u2014 Stefan moving-boundary problem"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "stefan_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_sensors",
      "SNR_dB",
      "latent_heat_error",
      "k_liquid_error",
      "k_solid_error",
      "supercool_error",
      "latent_heat_error",
      "k_liquid_error",
      "k_solid_error",
      "supercool_error"
    ],
    "allowed_problem_classes": [
      "stefan"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "stefan_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_sensors": 16,
        "SNR_dB": 30,
        "W": 128,
        "k_liquid_error": 0.0,
        "k_solid_error": 0.0,
        "latent_heat_error": 0.0,
        "supercool_error": 0.0
      },
      "problem_class": "stefan"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_sensors": [
        4,
        256
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "k_liquid_error": [
        0.0,
        0.1
      ],
      "k_solid_error": [
        0.0,
        0.1
      ],
      "latent_heat_error": [
        0.0,
        0.1
      ],
      "supercool_error": [
        0.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Latent-heat tracking (melt/solid boundary)",
  "title": "Phase Change Material \u2014 Stefan moving-boundary problem"
}

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