L1 ⚛ L1-310 ⊙ Testnet

Metropolis Monte Carlo

Computational Chemistry · Equilibrium configurational sampling

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⬇ principle.md ⬇ principle.json

Fork L1-310

⬇ L1-310.md ⬇ L1-310.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-310 (Metropolis Monte Carlo) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-310.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-310.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `O.ensemble_average` `int.stochastic` `E.potential_U` x + n,    n ~ 𝒩(0, σ²)

world state x (Boltzmann ensemble)

→

E · potential U `E.potential_U`

→

int · stochastic `int.stochastic`

→

O · ensemble average `O.ensemble_average`

→

observation y (none detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

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

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📋 JSON metadata

{
  "artifact_id": "L1-310",
  "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"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "observable_relative_error",
    "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": {
    "allowed_forward_operators": [
      "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": {
        "N_particles": 1000,
        "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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