L1 ⚛ L1-203 ⊙ Testnet

Thermoelectric Transport — coupled Seebeck-Peltier

Heat Transfer · ZT figure-of-merit inversion

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⬇ L1-203.md

# ⚛ L1 Principle — Thermoelectric Transport — coupled Seebeck-Peltier **ID:** `L1-203` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *ZT figure-of-merit inversion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** ZT materials map > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554035 --- ## 🧠 1. Introduction **Thermoelectric Transport — coupled Seebeck-Peltier** is a **linear inverse problem** whose unknown lives in **ZT materials map** space, within the **ZT figure-of-merit inversion** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **V T dual** sensing mechanism. The forward operator applies, in order: L · onsager coupling operator; L · peltier flux operator; L · seebeck emf operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · onsager coupling → L · peltier flux → L · seebeck emf → Frequency integration → **y** (detector). ``` y = ∫dω `L.seebeck_emf` `L.peltier_flux` `L.onsager_coupling` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.onsager_coupling` | L · onsager coupling operator | | `L.peltier_flux` | L · peltier flux operator | | `L.seebeck_emf` | L · seebeck emf operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | ZT figure-of-merit inversion | | Carrier | thermal | | Problem class | linear_inverse | | Solution space | ZT_materials_map | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 3 | | L dag | 3 | ## 📡 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:** `thermoelectric` · **Forward operator:** `thermoelectric_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | Snr db | dB | 30 | | N probes | — | 8 | | Alpha error | — | 0 | | Kappa error | — | 0 | | Sigma error | — | 0 | | Contact r error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 4 – 1500 | | Snr db | dB | 0 – 40 | | N probes | — | 2 – 64 | | Alpha error | — | 0.0 – 0.1 | | Kappa error | — | 0.0 – 0.1 | | Sigma error | — | 0.0 – 0.1 | | Contact r error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf50a819ca4064352b938656d6fe11da6cd5251cd370c125b1964aafb68b9f6a0` - **Chain tx hash:** `0x07250ddf0ef706b152bbd9cc2d64653cb028b34b97e0fef1a1dd8d764ab823a5` - **Chain block:** `41554035` --- ## File Mapping This bundle consists of: `L1-203.md`, `L1-203.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-203.md` | Source of truth — edit this | Human or LLM | | `L1-203.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 `L1-203`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-203.md).
Regenerate L1-203.json so every field matches the Markdown.
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L2-203-001 Thermoelectric Transport — coupled Seebeck-Peltier Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554035,
  "chain_hash": "0xf50a819ca4064352b938656d6fe11da6cd5251cd370c125b1964aafb68b9f6a0",
  "chain_tx_hash": "0x07250ddf0ef706b152bbd9cc2d64653cb028b34b97e0fef1a1dd8d764ab823a5",
  "domain": "Heat Transfer",
  "hardness_fn": {
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    "kappa": 240,
    "metric": "PSNR_dB",
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "thermal",
    "difficulty_delta": 3,
    "domain": "Heat Transfer",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.onsager_coupling",
      "L.peltier_flux",
      "L.seebeck_emf",
      "int.frequency"
    ],
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    "sensing_mechanism": "V_T_dual",
    "solution_space": "ZT_materials_map",
    "sub_domain": "ZT figure-of-merit inversion",
    "title": "Thermoelectric Transport \u2014 coupled Seebeck-Peltier"
  },
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    "allowed_problem_classes": [
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      "input_format": "measurement_only",
      "omega": {
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        "SNR_dB": 30,
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      "problem_class": "thermoelectric"
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    "omega_bounds": {
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      "T_K": [
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      ],
      "contact_R_error": [
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        0.3
      ],
      "kappa_error": [
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        0.1
      ],
      "sigma_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "ZT figure-of-merit inversion",
  "title": "Thermoelectric Transport \u2014 coupled Seebeck-Peltier"
}

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