L1 ⚛ L1-308 ⊙ Testnet

Free Energy Perturbation (FEP + TI + BAR)

Computational Chemistry · Alchemical free-energy methods

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⬇ L1-308.md

# ⚛ L1 Principle — Free Energy Perturbation (FEP + TI + BAR) **ID:** `L1-308` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *Alchemical free-energy methods* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** DG curve lambda > **📡 Carrier:** none · **🌫 Noise:** thermal langevin > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554115 --- ## 🧠 1. Introduction **Free Energy Perturbation (FEP + TI + BAR)** is a **nonlinear inverse problem** whose unknown lives in **DG curve lambda** space, within the **Alchemical free-energy methods** sub-domain of **Computational Chemistry**. Measurements consist of none via a **alchemical free energy** sensing mechanism. The forward operator applies, in order: E · alchemical hamiltonian operator; S · select operator; adds a prior term that biases the solution toward smoothness/sparsity; O · DG operator. Observations are corrupted by Langevin-type thermal fluctuations. Well-posed in principle; sampling convergence is practical bottleneck. ## ⚙ 2. Forward Model Physical chain: **x** → E · alchemical hamiltonian → S · select → O · DG → **y** (detector). ``` y = `O.DG` `S.select` `E.alchemical_hamiltonian` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.alchemical_hamiltonian` | E · alchemical hamiltonian operator | | `S.select` | S · select operator | | `O.DG` | O · dg operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Chemistry | | Sub domain | Alchemical free-energy methods | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | DG_curve_lambda | | Noise model | thermal_langevin | | Integration axis | lambda | | Difficulty delta | 5 | | L dag | 3.7 | ## 📡 4. Measurement Model Well-posed in principle; sampling convergence is practical bottleneck. | Metric | Value | |---|---| | Metric | DG_bind_error_kcal_mol | | Secondary | DG_solv_error_kcal_mol | ## 📏 5. Operating Range (Ω) **Center problem class:** `free_energy_perturbation` · **Forward operator:** `fep_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 298 | | N lambdas | — | 20 | | Softcore alpha | — | 0.5 | | N steps per lambda | — | 1e+06 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 200 – 400 | | N lambdas | — | 5 – 200 | | Softcore alpha | — | 0.1 – 1.0 | | N steps per lambda | — | 10000 – 1000000000.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** DG_bind <= 0.5 kcal/mol | Metric | Range | |---|---| | Dg bind error kcal mol | 0.1 – 10 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **DG_bind_error_kcal_mol**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x890766481cfe6ec2ef45315b1c5583e40a4570af1bd3c633542822fd2de679be` - **Chain tx hash:** `0x9748073561325005a11c280cc65a1e0ba54fad1abd074d5834e7084c1aacd3e2` - **Chain block:** `41554115` --- ## File Mapping This bundle consists of: `L1-308.md`, `L1-308.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-308.md` | Source of truth — edit this | Human or LLM | | `L1-308.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 `L1-308`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-308.md).
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📋 JSON metadata

{
  "artifact_id": "L1-308",
  "chain_block": 41554115,
  "chain_hash": "0x890766481cfe6ec2ef45315b1c5583e40a4570af1bd3c633542822fd2de679be",
  "chain_tx_hash": "0x9748073561325005a11c280cc65a1e0ba54fad1abd074d5834e7084c1aacd3e2",
  "domain": "Computational Chemistry",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "DG_bind_error_kcal_mol",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "DG_bind_error_kcal_mol",
    "regime": "Well-posed in principle; sampling convergence is practical bottleneck.",
    "secondary": "DG_solv_error_kcal_mol"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Computational Chemistry",
    "integration_axis": "lambda",
    "noise_model": "thermal_langevin",
    "primitives": [
      "E.alchemical_hamiltonian",
      "S.select",
      "O.regularize",
      "O.DG"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "alchemical_free_energy",
    "solution_space": "DG_curve_lambda",
    "sub_domain": "Alchemical free-energy methods",
    "title": "Free Energy Perturbation (FEP + TI + BAR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fep_forward"
    ],
    "allowed_omega_dimensions": [
      "N_lambdas",
      "N_steps_per_lambda",
      "softcore_alpha",
      "T_K"
    ],
    "allowed_problem_classes": [
      "free_energy_perturbation"
    ],
    "center_spec": {
      "epsilon_fn_center": "DG_bind \u003c= 0.5 kcal/mol",
      "forward_operator": "fep_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_lambdas": 20,
        "N_steps_per_lambda": 1000000.0,
        "T_K": 298,
        "softcore_alpha": 0.5
      },
      "problem_class": "free_energy_perturbation"
    },
    "epsilon_bounds": {
      "DG_bind_error_kcal_mol": [
        0.1,
        10
      ]
    },
    "omega_bounds": {
      "N_lambdas": [
        5,
        200
      ],
      "N_steps_per_lambda": [
        10000,
        1000000000.0
      ],
      "T_K": [
        200,
        400
      ],
      "softcore_alpha": [
        0.1,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Alchemical free-energy methods",
  "title": "Free Energy Perturbation (FEP + TI + BAR)"
}

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