L1 ⚛ L1-228 ⊙ Testnet

Thermoelasticity — coupled thermal-mechanical

Structural Mechanics · Classical weakly coupled thermoelasticity

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⬇ L1-228.md

# ⚛ L1 Principle — Thermoelasticity — coupled thermal-mechanical **ID:** `L1-228` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Classical weakly coupled thermoelasticity* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** u T coupled fields > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554023 --- ## 🧠 1. Introduction **Thermoelasticity — coupled thermal-mechanical** is a **linear inverse problem** whose unknown lives in **u T coupled fields** space, within the **Classical weakly coupled thermoelasticity** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **strain gauge thermocouple** sensing mechanism. The forward operator applies, in order: L · thermal strain operator; L · heat conduct operator; L · weak 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 · thermal strain → L · heat conduct → L · weak coupling → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.weak_coupling` `L.heat_conduct` `L.thermal_strain` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.thermal_strain` | L · thermal strain operator | | `L.heat_conduct` | L · heat conduct operator | | `L.weak_coupling` | L · weak coupling operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Classical weakly coupled thermoelasticity | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | u_T_coupled_fields | | Noise model | gaussian | | Integration axis | temporal | | 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:** `thermoelastic` · **Forward operator:** `thermoelastic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 10000 | | Snr db | dB | 30 | | E error | — | 0 | | N times | — | 500 | | K error | — | 0 | | Alpha t error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 100 – 1000000 | | Snr db | dB | 0 – 40 | | E error | — | 0.0 – 0.1 | | N times | — | 10 – 100000 | | K error | — | 0.0 – 0.1 | | Alpha t error | — | 0.0 – 0.1 | ## 🎯 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:** `0x87318e38ca5d45cbdf45ea099ec69faa9cc95c0d1cec2438c7d401b6833aad9b` - **Chain tx hash:** `0x663da3c87359cc0ddf398a86d12102d46afcfd48a19b044f934bfe1e20a5047a` - **Chain block:** `41554023` --- ## File Mapping This bundle consists of: `L1-228.md`, `L1-228.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-228.md` | Source of truth — edit this | Human or LLM | | `L1-228.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 `L1-228`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-228.md).
Regenerate L1-228.json so every field matches the Markdown.
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L2-228-001 Thermoelasticity — coupled thermal-mechanical Mismatch-Only Spec

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📋 JSON metadata

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    "integration_axis": "temporal",
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    "sensing_mechanism": "strain_gauge_thermocouple",
    "solution_space": "u_T_coupled_fields",
    "sub_domain": "Classical weakly coupled thermoelasticity",
    "title": "Thermoelasticity \u2014 coupled thermal-mechanical"
  },
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      "k_error": [
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Classical weakly coupled thermoelasticity",
  "title": "Thermoelasticity \u2014 coupled thermal-mechanical"
}

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