L1 ⚛ L1-309 ⊙ Testnet

Kinetic Monte Carlo (KMC)

Computational Chemistry · Rare-event stochastic dynamics

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⬇ L1-309.md

# ⚛ L1 Principle — Kinetic Monte Carlo (KMC) **ID:** `L1-309` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *Rare-event stochastic dynamics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** kmc trajectory ensemble > **📡 Carrier:** none · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554115 --- ## 🧠 1. Introduction **Kinetic Monte Carlo (KMC)** is a **nonlinear inverse problem** whose unknown lives in **kmc trajectory ensemble** space, within the **Rare-event stochastic dynamics** sub-domain of **Computational Chemistry**. Measurements consist of none via a **event sequence observable** sensing mechanism. The forward operator applies, in order: E · rate catalog operator; int · stochastic operator; O · trajectory distribution operator. Observations are corrupted by Poisson counting noise. Well-posed; Markov chain analysis gives eigenvalues of rate matrix. ## ⚙ 2. Forward Model Physical chain: **x** → E · rate catalog → int · stochastic → O · trajectory distribution → **y** (detector). ``` y = `O.trajectory_distribution` `int.stochastic` `E.rate_catalog` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.rate_catalog` | E · rate catalog operator | | `int.stochastic` | Int · stochastic operator | | `O.trajectory_distribution` | O · trajectory distribution operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Chemistry | | Sub domain | Rare-event stochastic dynamics | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | kmc_trajectory_ensemble | | Noise model | poisson | | Integration axis | time | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed; Markov chain analysis gives eigenvalues of rate matrix. | Metric | Value | |---|---| | Metric | rate_distribution_KL | | Secondary | first_passage_time_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `kinetic_monte_carlo` · **Forward operator:** `kmc_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 600 | | N events | — | 1e+06 | | N states | — | 1000 | | N rates per state | — | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 100 – 3000 | | N events | — | 1000 – 1000000000000.0 | | N states | — | 10 – 1000000000.0 | | N rates per state | — | 2 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** KL <= 0.03 | Metric | Range | |---|---| | Rate distribution kl | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **rate_distribution_KL**, with κ = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xaf6a09ab0a5c2131e4cf52d2256a0f21f3ab0da3861795c2743a92ca4506ffad` - **Chain tx hash:** `0xe61c632d17c8e852f738552e7867bf6b46a58dc3c10a8d2f5fcf74ace6496826` - **Chain block:** `41554115` --- ## File Mapping This bundle consists of: `L1-309.md`, `L1-309.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-309.md` | Source of truth — edit this | Human or LLM | | `L1-309.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 `L1-309`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-309.md).
Regenerate L1-309.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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L2-309-001 Kinetic Monte Carlo (KMC) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-309",
  "chain_block": 41554115,
  "chain_hash": "0xaf6a09ab0a5c2131e4cf52d2256a0f21f3ab0da3861795c2743a92ca4506ffad",
  "chain_tx_hash": "0xe61c632d17c8e852f738552e7867bf6b46a58dc3c10a8d2f5fcf74ace6496826",
  "domain": "Computational Chemistry",
  "hardness_fn": {
    "delta": 3,
    "kappa": 100,
    "metric": "rate_distribution_KL",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "rate_distribution_KL",
    "regime": "Well-posed; Markov chain analysis gives eigenvalues of rate matrix.",
    "secondary": "first_passage_time_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Computational Chemistry",
    "integration_axis": "time",
    "noise_model": "poisson",
    "primitives": [
      "E.rate_catalog",
      "int.stochastic",
      "O.trajectory_distribution"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "event_sequence_observable",
    "solution_space": "kmc_trajectory_ensemble",
    "sub_domain": "Rare-event stochastic dynamics",
    "title": "Kinetic Monte Carlo (KMC)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "kmc_forward"
    ],
    "allowed_omega_dimensions": [
      "N_states",
      "N_events",
      "T_K",
      "N_rates_per_state"
    ],
    "allowed_problem_classes": [
      "kinetic_monte_carlo"
    ],
    "center_spec": {
      "epsilon_fn_center": "KL \u003c= 0.03",
      "forward_operator": "kmc_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_events": 1000000.0,
        "N_rates_per_state": 10,
        "N_states": 1000,
        "T_K": 600
      },
      "problem_class": "kinetic_monte_carlo"
    },
    "epsilon_bounds": {
      "rate_distribution_KL": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "N_events": [
        1000,
        1000000000000.0
      ],
      "N_rates_per_state": [
        2,
        1000
      ],
      "N_states": [
        10,
        1000000000.0
      ],
      "T_K": [
        100,
        3000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rare-event stochastic dynamics",
  "title": "Kinetic Monte Carlo (KMC)"
}

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