L1 ⚛ L1-201 ⊙ Testnet

Conjugate Heat Transfer — coupled fluid-solid thermal

Heat Transfer · Fluid-solid interface heat flux matching

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⬇ principle.md ⬇ principle.json

Fork L1-201

⬇ L1-201.md ⬇ L1-201.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-201 (Conjugate Heat Transfer — coupled fluid-solid thermal) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-201.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-201.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.interface_coupling` `L.solid_conduction` `L.fluid_heat` x + n,    n ~ 𝒩(0, σ²)

world state x (coupled fluid solid temp)

→

L · fluid heat `L.fluid_heat`

→

L · solid conduction `L.solid_conduction`

→

L · interface coupling `L.interface_coupling`

→

Temporal integration ∫_t dt

→

observation y (thermal detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-201.md

# ⚛ L1 Principle — Conjugate Heat Transfer — coupled fluid-solid thermal **ID:** `L1-201` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *Fluid-solid interface heat flux matching* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** coupled fluid solid temp > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034 --- ## 🧠 1. Introduction **Conjugate Heat Transfer — coupled fluid-solid thermal** is a **nonlinear inverse problem** whose unknown lives in **coupled fluid solid temp** space, within the **Fluid-solid interface heat flux matching** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **ir pitot thermocouples** sensing mechanism. The forward operator applies, in order: L · fluid heat operator; L · solid conduction operator; L · interface coupling 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 · fluid heat → L · solid conduction → L · interface coupling → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.interface_coupling` `L.solid_conduction` `L.fluid_heat` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fluid_heat` | L · fluid heat operator | | `L.solid_conduction` | L · solid conduction operator | | `L.interface_coupling` | L · interface coupling operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | Fluid-solid interface heat flux matching | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | coupled_fluid_solid_temp | | 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:** `conjugate_ht` · **Forward operator:** `conjugate_ht_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N fluid | — | 10000 | | N solid | — | 10000 | | Wall k error | — | 0 | | Fluid kappa error | — | 0 | | Interface h error | — | 0 | | Contact resistance error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N fluid | — | 500 – 1000000 | | N solid | — | 500 – 500000 | | Wall k error | — | 0.0 – 0.1 | | Fluid kappa error | — | 0.0 – 0.1 | | Interface h error | — | 0.0 – 0.3 | | Contact resistance error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 21.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xee4ce3bbe6fa747fe6013b18610aba9d143e098a27cabd571ad4ac152e3e6605` - **Chain tx hash:** `0x34e21da0bfeacfafb8be77103aa1080f4ba12bf87a5c27dc778c9e060ec9006c` - **Chain block:** `41554034` --- ## File Mapping This bundle consists of: `L1-201.md`, `L1-201.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-201.md` | Source of truth — edit this | Human or LLM | | `L1-201.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 `L1-201`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

{
  "artifact_id": "L1-201",
  "chain_block": 41554034,
  "chain_hash": "0xee4ce3bbe6fa747fe6013b18610aba9d143e098a27cabd571ad4ac152e3e6605",
  "chain_tx_hash": "0x34e21da0bfeacfafb8be77103aa1080f4ba12bf87a5c27dc778c9e060ec9006c",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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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": "thermal",
    "difficulty_delta": 5,
    "domain": "Heat Transfer",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.fluid_heat",
      "L.solid_conduction",
      "L.interface_coupling",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "ir_pitot_thermocouples",
    "solution_space": "coupled_fluid_solid_temp",
    "sub_domain": "Fluid-solid interface heat flux matching",
    "title": "Conjugate Heat Transfer \u2014 coupled fluid-solid thermal"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "contact_resistance_error",
      "interface_h_error",
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      "fluid_kappa_error",
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    ],
    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "21.0",
      "forward_operator": "conjugate_ht_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_fluid": 10000,
        "N_solid": 10000,
        "SNR_dB": 30,
        "contact_resistance_error": 0.0,
        "fluid_kappa_error": 0.0,
        "interface_h_error": 0.0,
        "wall_k_error": 0.0
      },
      "problem_class": "conjugate_ht"
    },
    "epsilon_bounds": {
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        45.0
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    },
    "omega_bounds": {
      "N_fluid": [
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        1000000
      ],
      "N_solid": [
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      ],
      "SNR_dB": [
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      ],
      "contact_resistance_error": [
        0.0,
        0.5
      ],
      "fluid_kappa_error": [
        0.0,
        0.1
      ],
      "interface_h_error": [
        0.0,
        0.3
      ],
      "wall_k_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Fluid-solid interface heat flux matching",
  "title": "Conjugate Heat Transfer \u2014 coupled fluid-solid thermal"
}

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