L1 ⚛ L1-414 ⊙ Testnet

Gaussian Plume Atmospheric Dispersion

Environmental Science · Air quality modeling

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⬇ L1-414.md

# ⚛ L1 Principle — Gaussian Plume Atmospheric Dispersion **ID:** `L1-414` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Air quality modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** source strength location > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555220 --- ## 🧠 1. Introduction **Gaussian Plume Atmospheric Dispersion** is a **parameter-estimation problem** whose unknown lives in **source strength location** space, within the **Air quality modeling** sub-domain of **Environmental Science**. Measurements consist of N/A via a **atmospheric dispersion gaussian** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; O · least squares · source inversion operator; S · stability · pasquill gifford operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered source_strength_location 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 ~= 25); wind_direction_uncertainty_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → O · least squares · source inversion → S · stability · pasquill gifford → **y** (detector). ``` y = `S.stability.pasquill_gifford` `O.least_squares.source_inversion` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `O.least_squares.source_inversion` | O · least squares · source inversion operator | | `S.stability.pasquill_gifford` | S · stability · pasquill gifford operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Air quality modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | source_strength_location | | Noise model | lognormal | | Integration axis | downwind_distance | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered source_strength_location 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 ~= 25); wind_direction_uncertainty_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | source_strength_RMSE_percent | | Secondary | concentration_RMSE_ug_m3 | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `atmospheric_dispersion_gaussian` **Center point:** | Parameter | Unit | Value | |---|---|---| | N sensors | — | 20 | | Distance km | km | 1 | | Wind speed m s | s | 3 | | Stability class int | — | 4 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N sensors | — | 3 – 100 | | Distance km | km | 0.1 – 50.0 | | Wind speed m s | s | 0.5 – 10.0 | | Stability class int | — | 1 – 6 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25 source_strength_RMSE_percent | Metric | Range | |---|---| | Source strength rmse percent | 5 – 100 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **source_strength_RMSE_percent**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x88d1348556cbb501895c7b92d25f30ecb11f263bfadc08a1bac159057048fe95` - **Chain tx hash:** `0xf8ac93b16b2b9cc39d15fb24c59781512f4fc292f187e9326f3c1782b0bf6f3f` - **Chain block:** `41555220` --- ## File Mapping This bundle consists of: `L1-414.md`, `L1-414.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-414.md` | Source of truth — edit this | Human or LLM | | `L1-414.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 `L1-414`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-414.md).
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L2-414-001 Gaussian Plume Atmospheric Dispersion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_tx_hash": "0xf8ac93b16b2b9cc39d15fb24c59781512f4fc292f187e9326f3c1782b0bf6f3f",
  "domain": "Environmental Science",
  "hardness_fn": {
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    "kappa": 500,
    "metric": "source_strength_RMSE_percent",
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    "regime": "Existence of the recovered source_strength_location 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 ~= 25); wind_direction_uncertainty_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.",
    "secondary": "concentration_RMSE_ug_m3"
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    "L_DAG": 2.5,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Environmental Science",
    "integration_axis": "downwind_distance",
    "noise_model": "lognormal",
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      "O.least_squares.source_inversion",
      "S.stability.pasquill_gifford"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "atmospheric_dispersion_gaussian",
    "solution_space": "source_strength_location",
    "sub_domain": "Air quality modeling",
    "title": "Gaussian Plume Atmospheric Dispersion"
  },
  "size_tiers": {
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    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "25 source_strength_RMSE_percent",
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      "input_format": "measurement_only",
      "omega": {
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        "distance_km": 1.0,
        "stability_class_int": 4,
        "wind_speed_m_s": 3.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "source_strength_RMSE_percent": [
        5,
        100
      ]
    },
    "omega_bounds": {
      "N_sensors": [
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        100
      ],
      "distance_km": [
        0.1,
        50.0
      ],
      "stability_class_int": [
        1,
        6
      ],
      "wind_speed_m_s": [
        0.5,
        10.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Air quality modeling",
  "title": "Gaussian Plume Atmospheric Dispersion"
}

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