L1 ⚛ L1-416 ⊙ Testnet

Atmospheric Radiative Transfer Inversion

Environmental Science · Atmospheric optics

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⬇ principle.md ⬇ principle.json

Fork L1-416

⬇ L1-416.md ⬇ L1-416.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-416 (Atmospheric Radiative Transfer Inversion) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-416.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-416.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.optimal_estimation.rodgers` A `S.rt.disort_solver` x

world state x (1D atmospheric profile)

→

S · rt · disort solver `S.rt.disort_solver`

→

Generic linear operator A

→

O · optimal estimation · rodgers `O.optimal_estimation.rodgers`

→

observation y (photon detector)

Noise: thermally-driven Gaussian fluctuations

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-416.md

# ⚛ L1 Principle — Atmospheric Radiative Transfer Inversion **ID:** `L1-416` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Atmospheric optics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 1D atmospheric profile > **📡 Carrier:** photon · **🌫 Noise:** thermal gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555237 --- ## 🧠 1. Introduction **Atmospheric Radiative Transfer Inversion** is a **nonlinear inverse problem** whose unknown lives in **1D atmospheric profile** space, within the **Atmospheric optics** sub-domain of **Environmental Science**. Measurements consist of photons collected by an optical detector via a **satellite radiance inversion** sensing mechanism. The forward operator applies, in order: S · rt · disort solver operator; an unspecified linear measurement operator; O · optimal estimation · rodgers operator. Observations are corrupted by thermally-driven Gaussian fluctuations. Existence of the recovered 1D_atmospheric_profile 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 ~= 500); cloud_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · rt · disort solver → Generic linear operator → O · optimal estimation · rodgers → **y** (detector). ``` y = `O.optimal_estimation.rodgers` A `S.rt.disort_solver` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.rt.disort_solver` | S · rt · disort solver operator | | `L.linear_op` | An unspecified linear measurement operator | | `O.optimal_estimation.rodgers` | O · optimal estimation · rodgers operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Atmospheric optics | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 1D_atmospheric_profile | | Noise model | thermal_gaussian | | Integration axis | atmospheric_vertical | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 1D_atmospheric_profile 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 ~= 500); cloud_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | temperature_profile_RMSE_K | | Secondary | ozone_column_RMSE_DU | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `satellite_radiance_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | N layers | — | 40 | | N channels | — | 2000 | | Noise nedt k | — | 0.1 | | Cloud fraction | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N layers | — | 10 – 100 | | N channels | — | 100 – 10000 | | Noise nedt k | — | 0.01 – 1.0 | | Cloud fraction | — | 0.0 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.0 temperature_profile_RMSE_K | Metric | Range | |---|---| | Temperature profile rmse k | 0.2 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **temperature_profile_RMSE_K**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x53a2411a34f36493dcb8ffe795420c8dc1444016b1368196f04a654390b05c01` - **Chain tx hash:** `0x4a427b7da8a61f9e4f410f841b5658dd91672bb683e8e4db0491114a8e6ec6f9` - **Chain block:** `41555237` --- ## File Mapping This bundle consists of: `L1-416.md`, `L1-416.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-416.md` | Source of truth — edit this | Human or LLM | | `L1-416.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 `L1-416`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-416-001 Atmospheric Radiative Transfer Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-416",
  "chain_block": 41555237,
  "chain_hash": "0x53a2411a34f36493dcb8ffe795420c8dc1444016b1368196f04a654390b05c01",
  "chain_tx_hash": "0x4a427b7da8a61f9e4f410f841b5658dd91672bb683e8e4db0491114a8e6ec6f9",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000.0,
    "metric": "temperature_profile_RMSE_K",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "temperature_profile_RMSE_K",
    "regime": "Existence of the recovered 1D_atmospheric_profile 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 ~= 500); cloud_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.",
    "secondary": "ozone_column_RMSE_DU"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "atmospheric_vertical",
    "noise_model": "thermal_gaussian",
    "primitives": [
      "S.rt.disort_solver",
      "L.linear_op",
      "O.optimal_estimation.rodgers"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "satellite_radiance_inversion",
    "solution_space": "1D_atmospheric_profile",
    "sub_domain": "Atmospheric optics",
    "title": "Atmospheric Radiative Transfer Inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "satellite_radiance_inversion"
    ],
    "allowed_omega_dimensions": [
      "N_layers",
      "N_channels",
      "noise_NEdT_K",
      "cloud_fraction"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.0 temperature_profile_RMSE_K",
      "forward_operator": "satellite_radiance_inversion",
      "input_format": "measurement_only",
      "omega": {
        "N_channels": 2000,
        "N_layers": 40,
        "cloud_fraction": 0.0,
        "noise_NEdT_K": 0.1
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "temperature_profile_RMSE_K": [
        0.2,
        5.0
      ]
    },
    "omega_bounds": {
      "N_channels": [
        100,
        10000
      ],
      "N_layers": [
        10,
        100
      ],
      "cloud_fraction": [
        0.0,
        1.0
      ],
      "noise_NEdT_K": [
        0.01,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Atmospheric optics",
  "title": "Atmospheric Radiative Transfer Inversion"
}

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