L1 ⚛ L1-204 ⊙ Testnet

Thermal Contact Resistance — interface conductance estimation

Heat Transfer · Interface thermal conductance inversion

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⬇ principle.md ⬇ principle.json

Fork L1-204

⬇ L1-204.md ⬇ L1-204.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-204 (Thermal Contact Resistance — interface conductance estimation) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-204.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-204.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 = ∫_A dA `L.elliptic_solve` `L.interface_jump` `L.apply_flux` x + n,    n ~ 𝒩(0, σ²)

world state x (interface h map)

→

L · apply flux `L.apply_flux`

→

L · interface jump `L.interface_jump`

→

L · elliptic solve `L.elliptic_solve`

→

Spatial integration ∫_A dA

→

observation y (thermal detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-204.md

# ⚛ L1 Principle — Thermal Contact Resistance — interface conductance estimation **ID:** `L1-204` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *Interface thermal conductance inversion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** interface h map > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554035 --- ## 🧠 1. Introduction **Thermal Contact Resistance — interface conductance estimation** is a **linear inverse problem** whose unknown lives in **interface h map** space, within the **Interface thermal conductance inversion** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **thermocouples** sensing mechanism. The forward operator applies, in order: L · apply flux operator; L · interface jump operator; L · elliptic solve operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · apply flux → L · interface jump → L · elliptic solve → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.elliptic_solve` `L.interface_jump` `L.apply_flux` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.apply_flux` | L · apply flux operator | | `L.interface_jump` | L · interface jump operator | | `L.elliptic_solve` | L · elliptic solve operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | Interface thermal conductance inversion | | Carrier | thermal | | Problem class | linear_inverse | | Solution space | interface_h_map | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 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:** `contact_R` · **Forward operator:** `contact_R_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N probes | — | 8 | | K bulk error | — | 0 | | Pressure error | — | 0 | | Surface flatness error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N probes | — | 2 – 64 | | K bulk error | — | 0.0 – 0.1 | | Pressure error | — | 0.0 – 0.3 | | Surface flatness error | — | 0.0 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x378dcedb2275965deb03269efe4f35d2e149137362219f4f42b72d3f9dc2bdfb` - **Chain tx hash:** `0x5aa10eba986ed1b266a27b1003926be1c941ee8571a94807a01a9fde9e5eb6b6` - **Chain block:** `41554035` --- ## File Mapping This bundle consists of: `L1-204.md`, `L1-204.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-204.md` | Source of truth — edit this | Human or LLM | | `L1-204.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 `L1-204`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-204-001 Thermal Contact Resistance — interface conductance estimation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-204",
  "chain_block": 41554035,
  "chain_hash": "0x378dcedb2275965deb03269efe4f35d2e149137362219f4f42b72d3f9dc2bdfb",
  "chain_tx_hash": "0x5aa10eba986ed1b266a27b1003926be1c941ee8571a94807a01a9fde9e5eb6b6",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "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": 2.8,
    "carrier": "thermal",
    "difficulty_delta": 3,
    "domain": "Heat Transfer",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.apply_flux",
      "L.interface_jump",
      "L.elliptic_solve",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "thermocouples",
    "solution_space": "interface_h_map",
    "sub_domain": "Interface thermal conductance inversion",
    "title": "Thermal Contact Resistance \u2014 interface conductance estimation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "contact_R_forward"
    ],
    "allowed_omega_dimensions": [
      "N_probes",
      "SNR_dB",
      "surface_flatness_error",
      "k_bulk_error",
      "pressure_error",
      "surface_flatness_error",
      "k_bulk_error",
      "pressure_error"
    ],
    "allowed_problem_classes": [
      "contact_R"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "contact_R_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_probes": 8,
        "SNR_dB": 30,
        "k_bulk_error": 0.0,
        "pressure_error": 0.0,
        "surface_flatness_error": 0.0
      },
      "problem_class": "contact_R"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_probes": [
        2,
        64
      ],
      "SNR_dB": [
        0,
        40
      ],
      "k_bulk_error": [
        0.0,
        0.1
      ],
      "pressure_error": [
        0.0,
        0.3
      ],
      "surface_flatness_error": [
        0.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Interface thermal conductance inversion",
  "title": "Thermal Contact Resistance \u2014 interface conductance estimation"
}

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