L1 ⚛ L1-417 ⊙ Testnet

General Circulation Model (GCM) Inversion

Environmental Science · Climate modeling

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⬇ L1-417.md

# ⚛ L1 Principle — General Circulation Model (GCM) Inversion **ID:** `L1-417` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Climate modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** climate forcing parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41555238 --- ## 🧠 1. Introduction **General Circulation Model (GCM) Inversion** is a **parameter-estimation problem** whose unknown lives in **climate forcing parameter vector** space, within the **Climate modeling** sub-domain of **Environmental Science**. Measurements consist of N/A via a **climate model data assimilation** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · spectral · dynamical core operator; O · chi2 · reanalysis comparison operator. Observations are corrupted by observation gaussian. Existence of the recovered climate_forcing_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000000.0); internal_variability_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → S · spectral · dynamical core → O · chi2 · reanalysis comparison → **y** (detector). ``` y = `O.chi2.reanalysis_comparison` `S.spectral.dynamical_core` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.spectral.dynamical_core` | S · spectral · dynamical core operator | | `O.chi2.reanalysis_comparison` | O · chi2 · reanalysis comparison operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Climate modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | climate_forcing_parameter_vector | | Noise model | observation_gaussian | | Integration axis | global_atmosphere | | Difficulty delta | 10 | | L dag | 6 | ## 📡 4. Measurement Model Existence of the recovered climate_forcing_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000000.0); internal_variability_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | temperature_trend_RMSE_K_decade | | Secondary | precipitation_bias_mm_day | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `climate_model_data_assimilation` **Center point:** | Parameter | Unit | Value | |---|---|---| | Ecs k | — | 3 | | Simulation years | — | 100 | | N ensemble members | — | 100 | | Aerosol forcing wm2 | — | -1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Ecs k | — | 1.5 – 6.0 | | Simulation years | — | 10 – 1000 | | N ensemble members | — | 20 – 1000 | | Aerosol forcing wm2 | — | -3.0 – 0.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.1 temperature_trend_RMSE_K_decade | Metric | Range | |---|---| | Temperature trend rmse k decade | 0.02 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **temperature_trend_RMSE_K_decade**, with κ = `1000000000.0` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe9b17d6e35c477a9f8bb123aaf225389b1d66d7293ef6136668eb4d0cc2833b0` - **Chain tx hash:** `0x42865f7a14714976bdb0718971d6a58ec0c8ef8fe44aad433ad6c3fcafdff2fa` - **Chain block:** `41555238` --- ## File Mapping This bundle consists of: `L1-417.md`, `L1-417.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-417.md` | Source of truth — edit this | Human or LLM | | `L1-417.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 `L1-417`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-417.md).
Regenerate L1-417.json so every field matches the Markdown.
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L2-417-001 General Circulation Model (GCM) Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555238,
  "chain_hash": "0xe9b17d6e35c477a9f8bb123aaf225389b1d66d7293ef6136668eb4d0cc2833b0",
  "chain_tx_hash": "0x42865f7a14714976bdb0718971d6a58ec0c8ef8fe44aad433ad6c3fcafdff2fa",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 10,
    "kappa": 1000000000.0,
    "metric": "temperature_trend_RMSE_K_decade",
    "type": "epsilon_fn"
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  "observable_profile": {
    "metric": "temperature_trend_RMSE_K_decade",
    "regime": "Existence of the recovered climate_forcing_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000000.0); internal_variability_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "precipitation_bias_mm_day"
  },
  "physics_fingerprint": {
    "L_DAG": 6.0,
    "carrier": "N/A",
    "difficulty_delta": 10,
    "domain": "Environmental Science",
    "integration_axis": "global_atmosphere",
    "noise_model": "observation_gaussian",
    "primitives": [
      "D.space",
      "S.spectral.dynamical_core",
      "O.chi2.reanalysis_comparison"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "climate_model_data_assimilation",
    "solution_space": "climate_forcing_parameter_vector",
    "sub_domain": "Climate modeling",
    "title": "General Circulation Model (GCM) Inversion"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "simulation_years",
      "aerosol_forcing_Wm2",
      "ECS_K"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.1 temperature_trend_RMSE_K_decade",
      "forward_operator": "climate_model_data_assimilation",
      "input_format": "measurement_only",
      "omega": {
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        "N_ensemble_members": 100,
        "aerosol_forcing_Wm2": -1.0,
        "simulation_years": 100
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "temperature_trend_RMSE_K_decade": [
        0.02,
        0.5
      ]
    },
    "omega_bounds": {
      "ECS_K": [
        1.5,
        6.0
      ],
      "N_ensemble_members": [
        20,
        1000
      ],
      "aerosol_forcing_Wm2": [
        -3.0,
        0.0
      ],
      "simulation_years": [
        10,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Climate modeling",
  "title": "General Circulation Model (GCM) Inversion"
}

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