L1 ⚛ L1-331 ⊙ Testnet

Grain Growth and Recrystallization

Materials Science · Microstructure evolution

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⬇ L1-331.md

# ⚛ L1 Principle — Grain Growth and Recrystallization **ID:** `L1-331` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Microstructure evolution* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** grain orientation map > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554128 --- ## 🧠 1. Introduction **Grain Growth and Recrystallization** is a **nonlinear inverse problem** whose unknown lives in **grain orientation map** space, within the **Microstructure evolution** sub-domain of **Materials Science**. Measurements consist of none via a **ebsd micrograph** sensing mechanism. The forward operator applies, in order: E · curvature flow operator; adds a prior term that biases the solution toward smoothness/sparsity; O · grain statistics operator. Observations are corrupted by additive Gaussian noise. Well-posed; parabolic in mean-field; statistical fluctuations bounded. ## ⚙ 2. Forward Model Physical chain: **x** → E · curvature flow → O · grain statistics → **y** (detector). ``` y = `O.grain_statistics` `E.curvature_flow` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.curvature_flow` | E · curvature flow operator | | `O.grain_statistics` | O · grain statistics operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Microstructure evolution | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | grain_orientation_map | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 3 | | L dag | 3.1 | ## 📡 4. Measurement Model Well-posed; parabolic in mean-field; statistical fluctuations bounded. | Metric | Value | |---|---| | Metric | grain_size_relative_error | | Secondary | texture_KL_divergence | ## 📏 5. Operating Range (Ω) **Center problem class:** `grain_growth` · **Forward operator:** `grain_growth_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 1000 | | Grid n | N | 256 | | F pinning | — | 0 | | T anneal s | s | 100 | | Initial grains | — | 10000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 300 – 2000 | | Grid n | N | 64 – 2048 | | F pinning | — | 0 – 0.2 | | T anneal s | s | 1 – 100000 | | Initial grains | — | 100 – 1000000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** <r> rel error <= 0.04 | Metric | Range | |---|---| | Grain size relative error | 0.01 – 0.4 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **grain_size_relative_error**, with κ = `150` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe452da87a79ee73252faff58d86558b28a575cd76ffd77c983cae44f0700e925` - **Chain tx hash:** `0x86bdfac8e9db203afe5c6644a7f12906b5ede8a14f3772155cd71c889acd5183` - **Chain block:** `41554128` --- ## File Mapping This bundle consists of: `L1-331.md`, `L1-331.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-331.md` | Source of truth — edit this | Human or LLM | | `L1-331.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 `L1-331`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-331.md).
Regenerate L1-331.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-331-001 Grain Growth and Recrystallization Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554128,
  "chain_hash": "0xe452da87a79ee73252faff58d86558b28a575cd76ffd77c983cae44f0700e925",
  "chain_tx_hash": "0x86bdfac8e9db203afe5c6644a7f12906b5ede8a14f3772155cd71c889acd5183",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 3,
    "kappa": 150,
    "metric": "grain_size_relative_error",
    "type": "epsilon_fn"
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      "name": "primary",
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  "observable_profile": {
    "metric": "grain_size_relative_error",
    "regime": "Well-posed; parabolic in mean-field; statistical fluctuations bounded.",
    "secondary": "texture_KL_divergence"
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  "physics_fingerprint": {
    "L_DAG": 3.1,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Materials Science",
    "integration_axis": "time",
    "noise_model": "gaussian",
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    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "ebsd_micrograph",
    "solution_space": "grain_orientation_map",
    "sub_domain": "Microstructure evolution",
    "title": "Grain Growth and Recrystallization"
  },
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    "allowed_problem_classes": [
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    "center_spec": {
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      "omega": {
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        "initial_grains": 10000,
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      "problem_class": "grain_growth"
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    "epsilon_bounds": {
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        0.01,
        0.4
      ]
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    "omega_bounds": {
      "T_K": [
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        2000
      ],
      "f_pinning": [
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        0.2
      ],
      "grid_N": [
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        2048
      ],
      "initial_grains": [
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        1000000
      ],
      "t_anneal_s": [
        1,
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Microstructure evolution",
  "title": "Grain Growth and Recrystallization"
}

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