L1 ⚛ L1-310 ⊙ Testnet

Metropolis Monte Carlo

Computational Chemistry · Equilibrium configurational sampling

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⬇ L1-310.md

# ⚛ L1 Principle — Metropolis Monte Carlo **ID:** `L1-310` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *Equilibrium configurational sampling* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** Boltzmann ensemble > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554115 --- ## 🧠 1. Introduction **Metropolis Monte Carlo** is a **linear inverse problem** whose unknown lives in **Boltzmann ensemble** space, within the **Equilibrium configurational sampling** sub-domain of **Computational Chemistry**. Measurements consist of none via a **ensemble observable** sensing mechanism. The forward operator applies, in order: E · potential U operator; int · stochastic operator; O · ensemble average operator. Observations are corrupted by additive Gaussian noise. Well-posed; ergodicity + detailed balance ensure convergence. ## ⚙ 2. Forward Model Physical chain: **x** → E · potential U → int · stochastic → O · ensemble average → **y** (detector). ``` y = `O.ensemble_average` `int.stochastic` `E.potential_U` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.potential_U` | E · potential u operator | | `int.stochastic` | Int · stochastic operator | | `O.ensemble_average` | O · ensemble average operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Chemistry | | Sub domain | Equilibrium configurational sampling | | Carrier | none | | Problem class | linear_inverse | | Solution space | Boltzmann_ensemble | | Noise model | gaussian | | Integration axis | mc_steps | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed; ergodicity + detailed balance ensure convergence. | Metric | Value | |---|---| | Metric | observable_relative_error | | Secondary | autocorrelation_time | ## 📏 5. Operating Range (Ω) **Center problem class:** `monte_carlo_metropolis` · **Forward operator:** `metropolis_mc_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | N sweeps | — | 1e+06 | | Ensemble | — | NVT | | N particles | — | 1000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 1 – 10000 | | N sweeps | — | 10000 – 10000000000.0 | | Ensemble | — | NVT, NPT, GCMC, Gibbs | | N particles | — | 10 – 10000000.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** observable rel error <= 0.02 | Metric | Range | |---|---| | Observable relative error | 0.005 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **observable_relative_error**, with κ = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x98eab4dc52f93d074d6742458d1cb041fe58fed198ce87d0cdd6431f0b113b88` - **Chain tx hash:** `0x7af301dfb644e5a15bc354a486da48fa9a2c41047d5413a7648d3813653e8b98` - **Chain block:** `41554115` --- ## File Mapping This bundle consists of: `L1-310.md`, `L1-310.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-310.md` | Source of truth — edit this | Human or LLM | | `L1-310.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 `L1-310`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-310.md).
Regenerate L1-310.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-310-001 Metropolis Monte Carlo Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554115,
  "chain_hash": "0x98eab4dc52f93d074d6742458d1cb041fe58fed198ce87d0cdd6431f0b113b88",
  "chain_tx_hash": "0x7af301dfb644e5a15bc354a486da48fa9a2c41047d5413a7648d3813653e8b98",
  "domain": "Computational Chemistry",
  "hardness_fn": {
    "delta": 3,
    "kappa": 100,
    "metric": "observable_relative_error",
    "type": "epsilon_fn"
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  "layer": "L1",
  "observable_profile": {
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    "regime": "Well-posed; ergodicity + detailed balance ensure convergence.",
    "secondary": "autocorrelation_time"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Computational Chemistry",
    "integration_axis": "mc_steps",
    "noise_model": "gaussian",
    "primitives": [
      "E.potential_U",
      "int.stochastic",
      "O.ensemble_average"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "ensemble_observable",
    "solution_space": "Boltzmann_ensemble",
    "sub_domain": "Equilibrium configurational sampling",
    "title": "Metropolis Monte Carlo"
  },
  "size_tiers": {
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      "metropolis_mc_forward"
    ],
    "allowed_omega_dimensions": [
      "N_particles",
      "N_sweeps",
      "T_K",
      "ensemble"
    ],
    "allowed_problem_classes": [
      "monte_carlo_metropolis"
    ],
    "center_spec": {
      "epsilon_fn_center": "observable rel error \u003c= 0.02",
      "forward_operator": "metropolis_mc_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_sweeps": 1000000.0,
        "T_K": 300,
        "ensemble": "NVT"
      },
      "problem_class": "monte_carlo_metropolis"
    },
    "epsilon_bounds": {
      "observable_relative_error": [
        0.005,
        0.3
      ]
    },
    "omega_bounds": {
      "N_particles": [
        10,
        10000000.0
      ],
      "N_sweeps": [
        10000,
        10000000000.0
      ],
      "T_K": [
        1,
        10000
      ],
      "ensemble": [
        "NVT",
        "NPT",
        "GCMC",
        "Gibbs"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Equilibrium configurational sampling",
  "title": "Metropolis Monte Carlo"
}

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