L1 ⚛ L1-337 ⊙ Testnet

Thin Film Growth Kinetics

Materials Science · Nucleation-growth-coalescence

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⬇ L1-337.md

# ⚛ L1 Principle — Thin Film Growth Kinetics **ID:** `L1-337` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Nucleation-growth-coalescence* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** film morphology island distribution > **📡 Carrier:** none · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554129 --- ## 🧠 1. Introduction **Thin Film Growth Kinetics** is a **nonlinear inverse problem** whose unknown lives in **film morphology island distribution** space, within the **Nucleation-growth-coalescence** sub-domain of **Materials Science**. Measurements consist of none via a **rheed afm insitu** sensing mechanism. The forward operator applies, in order: E · deposition flux operator; E · surface diffusion operator; applies a smooth nonlinear function element-wise; O · film morphology operator. Observations are corrupted by Poisson counting noise. Well-posed forward; inversion of (D, E_mig) from N(s,t) moderately ill-conditioned (Arrhenius vs pre-factor). ## ⚙ 2. Forward Model Physical chain: **x** → E · deposition flux → E · surface diffusion → Pointwise nonlinearity → O · film morphology → **y** (detector). ``` y = `O.film_morphology` f(·) `E.surface_diffusion` `E.deposition_flux` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.deposition_flux` | E · deposition flux operator | | `E.surface_diffusion` | E · surface diffusion operator | | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.film_morphology` | O · film morphology operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Nucleation-growth-coalescence | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | film_morphology_island_distribution | | Noise model | poisson | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.7 | ## 📡 4. Measurement Model Well-posed forward; inversion of (D, E_mig) from N(s,t) moderately ill-conditioned (Arrhenius vs pre-factor). | Metric | Value | |---|---| | Metric | island_density_relative_error | | Secondary | roughness_rms_error_nm | ## 📏 5. Operating Range (Ω) **Center problem class:** `thin_film_growth` · **Forward operator:** `thinfilm_kmc_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 500 | | T s | s | 10 | | F ml s | s | 0.1 | | E mig ev | — | 0.8 | | Lattice l | — | 1024 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 200 – 1500 | | T s | s | 0.1 – 3600 | | F ml s | s | 0.0001 – 10 | | E mig ev | — | 0.1 – 2.5 | | Lattice l | — | 128 – 8192 | ## 🎯 6. Tolerance (ε) **Center tolerance:** island density rel error <= 0.05 | Metric | Range | |---|---| | Island density relative error | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **island_density_relative_error**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xd081498a3276ff5939256a9779e12660f541ce2186d7cbdce273e5fcb121cb1e` - **Chain tx hash:** `0xeb4df93a151b6acab71b5a4cbb88cedeb85ab6ea5e7fcef7d8b147bbefb5746d` - **Chain block:** `41554129` --- ## File Mapping This bundle consists of: `L1-337.md`, `L1-337.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-337.md` | Source of truth — edit this | Human or LLM | | `L1-337.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 `L1-337`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-337.md).
Regenerate L1-337.json so every field matches the Markdown.
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📋 JSON metadata

{
  "artifact_id": "L1-337",
  "chain_block": 41554129,
  "chain_hash": "0xd081498a3276ff5939256a9779e12660f541ce2186d7cbdce273e5fcb121cb1e",
  "chain_tx_hash": "0xeb4df93a151b6acab71b5a4cbb88cedeb85ab6ea5e7fcef7d8b147bbefb5746d",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "island_density_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "island_density_relative_error",
    "regime": "Well-posed forward; inversion of (D, E_mig) from N(s,t) moderately ill-conditioned (Arrhenius vs pre-factor).",
    "secondary": "roughness_rms_error_nm"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Materials Science",
    "integration_axis": "time",
    "noise_model": "poisson",
    "primitives": [
      "E.deposition_flux",
      "E.surface_diffusion",
      "N.pointwise",
      "O.film_morphology"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "rheed_afm_insitu",
    "solution_space": "film_morphology_island_distribution",
    "sub_domain": "Nucleation-growth-coalescence",
    "title": "Thin Film Growth Kinetics"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "thinfilm_kmc_forward"
    ],
    "allowed_omega_dimensions": [
      "F_ML_s",
      "T_K",
      "t_s",
      "lattice_L",
      "E_mig_eV"
    ],
    "allowed_problem_classes": [
      "thin_film_growth"
    ],
    "center_spec": {
      "epsilon_fn_center": "island density rel error \u003c= 0.05",
      "forward_operator": "thinfilm_kmc_forward",
      "input_format": "measurement_only",
      "omega": {
        "E_mig_eV": 0.8,
        "F_ML_s": 0.1,
        "T_K": 500,
        "lattice_L": 1024,
        "t_s": 10
      },
      "problem_class": "thin_film_growth"
    },
    "epsilon_bounds": {
      "island_density_relative_error": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "E_mig_eV": [
        0.1,
        2.5
      ],
      "F_ML_s": [
        0.0001,
        10
      ],
      "T_K": [
        200,
        1500
      ],
      "lattice_L": [
        128,
        8192
      ],
      "t_s": [
        0.1,
        3600
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Nucleation-growth-coalescence",
  "title": "Thin Film Growth Kinetics"
}

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