L1 ⚛ L1-334 ⊙ Testnet

Dendritic Solidification

Materials Science · Phase-field solidification

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⬇ L1-334.md

# ⚛ L1 Principle — Dendritic Solidification **ID:** `L1-334` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Phase-field solidification* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** dendrite morphology and temperature > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554128 --- ## 🧠 1. Introduction **Dendritic Solidification** is a **nonlinear inverse problem** whose unknown lives in **dendrite morphology and temperature** space, within the **Phase-field solidification** sub-domain of **Materials Science**. Measurements consist of none via a **insitu imaging X ray synchrotron** sensing mechanism. The forward operator applies, in order: E · phi evolution operator; E · thermal diffusion operator; a fixed-point or gradient iteration on the unknown; O · dendrite morphology operator. Observations are corrupted by additive Gaussian noise. Stiff reaction-diffusion; well-posed under Karma-Rappel anti-trapping; inversion from morphology is moderate-ill-conditioned. ## ⚙ 2. Forward Model Physical chain: **x** → E · phi evolution → E · thermal diffusion → O · dendrite morphology → **y** (detector). ``` y = `O.dendrite_morphology` `E.thermal_diffusion` `E.phi_evolution` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.phi_evolution` | E · phi evolution operator | | `E.thermal_diffusion` | E · thermal diffusion operator | | `O.dendrite_morphology` | O · dendrite morphology operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Phase-field solidification | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | dendrite_morphology_and_temperature | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Stiff reaction-diffusion; well-posed under Karma-Rappel anti-trapping; inversion from morphology is moderate-ill-conditioned. | Metric | Value | |---|---| | Metric | dendrite_tip_velocity_relative_error | | Secondary | arm_spacing_error_um | ## 📏 5. Operating Range (Ω) **Center problem class:** `solidification` · **Forward operator:** `solidification_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Dt k | — | 5 | | Grid n | N | 512 | | V pull um s | s | 100 | | K partition | — | 0.15 | | Lambda 1 um | µm | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Dt k | — | 0.1 – 100 | | Grid n | N | 128 – 4096 | | V pull um s | s | 1 – 10000 | | K partition | — | 0.01 – 0.99 | | Lambda 1 um | µm | 1 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** tip velocity rel error <= 0.05 | Metric | Range | |---|---| | Dendrite tip velocity relative error | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **dendrite_tip_velocity_relative_error**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9deaf9dd67d72f543ca6acdbff2197e1517826064235e3deca58f47255a5e55e` - **Chain tx hash:** `0x5807e5796a1d240c02c89c781f4146a64ce7d6dfd314106b7415b388b6c21489` - **Chain block:** `41554128` --- ## File Mapping This bundle consists of: `L1-334.md`, `L1-334.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-334.md` | Source of truth — edit this | Human or LLM | | `L1-334.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 `L1-334`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-334.md).
Regenerate L1-334.json so every field matches the Markdown.
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L2-334-001 Dendritic Solidification Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-334",
  "chain_block": 41554128,
  "chain_hash": "0x9deaf9dd67d72f543ca6acdbff2197e1517826064235e3deca58f47255a5e55e",
  "chain_tx_hash": "0x5807e5796a1d240c02c89c781f4146a64ce7d6dfd314106b7415b388b6c21489",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "dendrite_tip_velocity_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "dendrite_tip_velocity_relative_error",
    "regime": "Stiff reaction-diffusion; well-posed under Karma-Rappel anti-trapping; inversion from morphology is moderate-ill-conditioned.",
    "secondary": "arm_spacing_error_um"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Materials Science",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.phi_evolution",
      "E.thermal_diffusion",
      "O.iter",
      "O.dendrite_morphology"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "insitu_imaging_X_ray_synchrotron",
    "solution_space": "dendrite_morphology_and_temperature",
    "sub_domain": "Phase-field solidification",
    "title": "Dendritic Solidification"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "solidification_forward"
    ],
    "allowed_omega_dimensions": [
      "grid_N",
      "lambda_1_um",
      "V_pull_um_s",
      "dT_K",
      "k_partition"
    ],
    "allowed_problem_classes": [
      "solidification"
    ],
    "center_spec": {
      "epsilon_fn_center": "tip velocity rel error \u003c= 0.05",
      "forward_operator": "solidification_forward",
      "input_format": "measurement_only",
      "omega": {
        "V_pull_um_s": 100,
        "dT_K": 5,
        "grid_N": 512,
        "k_partition": 0.15,
        "lambda_1_um": 20
      },
      "problem_class": "solidification"
    },
    "epsilon_bounds": {
      "dendrite_tip_velocity_relative_error": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "V_pull_um_s": [
        1,
        10000
      ],
      "dT_K": [
        0.1,
        100
      ],
      "grid_N": [
        128,
        4096
      ],
      "k_partition": [
        0.01,
        0.99
      ],
      "lambda_1_um": [
        1,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Phase-field solidification",
  "title": "Dendritic Solidification"
}

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