L1 ⚛ L1-420 ⊙ Testnet

Sea Ice Thermodynamic-Dynamic Inversion

Environmental Science · Cryosphere modeling

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⬇ L1-420.md

# ⚛ L1 Principle — Sea Ice Thermodynamic-Dynamic Inversion **ID:** `L1-420` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Cryosphere modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** sea ice state vector > **📡 Carrier:** photon · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **Sea Ice Thermodynamic-Dynamic Inversion** is a **parameter-estimation problem** whose unknown lives in **sea ice state vector** space, within the **Cryosphere modeling** sub-domain of **Environmental Science**. Measurements consist of photons collected by an optical detector via a **passive microwave sea ice** sensing mechanism. The forward operator applies, in order: S · passive microwave · brightness temp operator; gradient / divergence with respect to position; O · chi2 · sia sie operator. Observations are corrupted by measurement gaussian. Existence of the recovered sea_ice_state_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 ~= 200); melt_pond_fraction dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · passive microwave · brightness temp → Spatial derivative → O · chi2 · sia sie → **y** (detector). ``` y = `O.chi2.sia_sie` ∇ `S.passive_microwave.brightness_temp` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.passive_microwave.brightness_temp` | S · passive microwave · brightness temp operator | | `D.space` | Gradient / divergence with respect to position | | `O.chi2.sia_sie` | O · chi2 · sia sie operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Cryosphere modeling | | Carrier | photon | | Problem class | parameter_estimation | | Solution space | sea_ice_state_vector | | Noise model | measurement_gaussian | | Integration axis | sea_ice_extent | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered sea_ice_state_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 ~= 200); melt_pond_fraction dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | sea_ice_concentration_RMSE_percent | | Secondary | thickness_RMSE_m | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `passive_microwave_sea_ice` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snow depth cm | — | 20 | | N swath pixels | — | 10000 | | Melt pond fraction | — | 0 | | Ice concentration percent | — | 80 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snow depth cm | — | 0 – 100 | | N swath pixels | — | 1000 – 1000000 | | Melt pond fraction | — | 0.0 – 0.5 | | Ice concentration percent | — | 0 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5 sea_ice_concentration_RMSE_percent | Metric | Range | |---|---| | Sea ice concentration rmse percent | 1 – 20 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **sea_ice_concentration_RMSE_percent**, with κ = `5000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x83fac7ae18b99e3c24a44877225938126d15317b2a89d83193959c8f88a5b8b0` - **Chain tx hash:** `0x4a3e567baaabd23c365a21182d55b091546ab48d9703ec24753f92fe3fa18cef` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-420.md`, `L1-420.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-420.md` | Source of truth — edit this | Human or LLM | | `L1-420.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 `L1-420`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-420.md).
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L2-420-001 Sea Ice Thermodynamic-Dynamic Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-420",
  "chain_block": 41555239,
  "chain_hash": "0x83fac7ae18b99e3c24a44877225938126d15317b2a89d83193959c8f88a5b8b0",
  "chain_tx_hash": "0x4a3e567baaabd23c365a21182d55b091546ab48d9703ec24753f92fe3fa18cef",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 5000,
    "metric": "sea_ice_concentration_RMSE_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "sea_ice_concentration_RMSE_percent",
    "regime": "Existence of the recovered sea_ice_state_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 ~= 200); melt_pond_fraction dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "thickness_RMSE_m"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "sea_ice_extent",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "S.passive_microwave.brightness_temp",
      "D.space",
      "O.chi2.sia_sie"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "passive_microwave_sea_ice",
    "solution_space": "sea_ice_state_vector",
    "sub_domain": "Cryosphere modeling",
    "title": "Sea Ice Thermodynamic-Dynamic Inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "passive_microwave_sea_ice"
    ],
    "allowed_omega_dimensions": [
      "N_swath_pixels",
      "ice_concentration_percent",
      "snow_depth_cm",
      "melt_pond_fraction"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "5 sea_ice_concentration_RMSE_percent",
      "forward_operator": "passive_microwave_sea_ice",
      "input_format": "measurement_only",
      "omega": {
        "N_swath_pixels": 10000,
        "ice_concentration_percent": 80,
        "melt_pond_fraction": 0.0,
        "snow_depth_cm": 20
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "sea_ice_concentration_RMSE_percent": [
        1,
        20
      ]
    },
    "omega_bounds": {
      "N_swath_pixels": [
        1000,
        1000000
      ],
      "ice_concentration_percent": [
        0,
        100
      ],
      "melt_pond_fraction": [
        0.0,
        0.5
      ],
      "snow_depth_cm": [
        0,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cryosphere modeling",
  "title": "Sea Ice Thermodynamic-Dynamic Inversion"
}

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