L1 ⚛ L1-332 ⊙ Testnet

Classical Nucleation Theory

Materials Science · Nucleation kinetics

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⬇ L1-332.md

# ⚛ L1 Principle — Classical Nucleation Theory **ID:** `L1-332` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Nucleation kinetics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** J T Dmu surface > **📡 Carrier:** none · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554128 --- ## 🧠 1. Introduction **Classical Nucleation Theory** is a **nonlinear inverse problem** whose unknown lives in **J T Dmu surface** space, within the **Nucleation kinetics** sub-domain of **Materials Science**. Measurements consist of none via a **induction time measurement** sensing mechanism. The forward operator applies, in order: E · cluster thermodynamics operator; E · nucleation barrier operator; K · filter operator; O · J rate operator. Observations are corrupted by Poisson counting noise. Well-posed forward; J is exponentially sensitive to sigma, making inversion challenging. ## ⚙ 2. Forward Model Physical chain: **x** → E · cluster thermodynamics → E · nucleation barrier → O · J rate → **y** (detector). ``` y = `O.J_rate` `E.nucleation_barrier` `E.cluster_thermodynamics` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.cluster_thermodynamics` | E · cluster thermodynamics operator | | `E.nucleation_barrier` | E · nucleation barrier operator | | `O.J_rate` | O · j rate operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `K.filter` | K · filter operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Nucleation kinetics | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | J_T_Dmu_surface | | Noise model | poisson | | Integration axis | temperature | | Difficulty delta | 3 | | L dag | 3.1 | ## 📡 4. Measurement Model Well-posed forward; J is exponentially sensitive to sigma, making inversion challenging. | Metric | Value | |---|---| | Metric | log_J_relative_error | | Secondary | tau_induction_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `classical_nucleation` · **Forward operator:** `cnt_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N sites | — | 1000000000000000000000 | | Dmu kjmol | — | 2 | | T under k | — | 10 | | Interface sigma mjm2 | — | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N sites | — | 1000000000000000.0 – 10000000000000000000000000 | | Dmu kjmol | — | 0.1 – 20 | | T under k | — | 0.1 – 200 | | Interface sigma mjm2 | — | 10 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** log10(J) error <= 0.3 | Metric | Range | |---|---| | Log j relative error | 0.1 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **log_J_relative_error**, with κ = `120` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf8b48cb50eb6adae4d9bd09c2921ffcdd77f5db6e1956136eb7dd7c3d68bb6e3` - **Chain tx hash:** `0xc11fbb15792fba74fd7d2148570cfbad3f814a325e6c3051f0ee2f28fbe1ac70` - **Chain block:** `41554128` --- ## File Mapping This bundle consists of: `L1-332.md`, `L1-332.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-332.md` | Source of truth — edit this | Human or LLM | | `L1-332.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 `L1-332`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-332.md).
Regenerate L1-332.json so every field matches the Markdown.
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L2-332-001 Classical Nucleation Theory Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554128,
  "chain_hash": "0xf8b48cb50eb6adae4d9bd09c2921ffcdd77f5db6e1956136eb7dd7c3d68bb6e3",
  "chain_tx_hash": "0xc11fbb15792fba74fd7d2148570cfbad3f814a325e6c3051f0ee2f28fbe1ac70",
  "domain": "Materials Science",
  "hardness_fn": {
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  "observable_profile": {
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    "secondary": "tau_induction_error"
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  "physics_fingerprint": {
    "L_DAG": 3.1,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Materials Science",
    "integration_axis": "temperature",
    "noise_model": "poisson",
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    ],
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    "sensing_mechanism": "induction_time_measurement",
    "solution_space": "J_T_Dmu_surface",
    "sub_domain": "Nucleation kinetics",
    "title": "Classical Nucleation Theory"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "Dmu_kJmol",
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    "allowed_problem_classes": [
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      "input_format": "measurement_only",
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        "T_under_K": 10,
        "interface_sigma_mJm2": 100
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      "problem_class": "classical_nucleation"
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        0.1,
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    "omega_bounds": {
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        0.1,
        20
      ],
      "N_sites": [
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        10000000000000000000000000
      ],
      "T_under_K": [
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        200
      ],
      "interface_sigma_mJm2": [
        10,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Nucleation kinetics",
  "title": "Classical Nucleation Theory"
}

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