L1 ⚛ L1-425 ⊙ Testnet

Groundwater Contaminant Transport Inversion

Environmental Science · Subsurface hydrology

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⬇ L1-425.md

# ⚛ L1 Principle — Groundwater Contaminant Transport Inversion **ID:** `L1-425` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Subsurface hydrology* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D hydraulic conductivity > **📡 Carrier:** N/A · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **Groundwater Contaminant Transport Inversion** is a **nonlinear inverse problem** whose unknown lives in **3D hydraulic conductivity** space, within the **Subsurface hydrology** sub-domain of **Environmental Science**. Measurements consist of N/A via a **groundwater monitoring network** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · ade · solute transport operator; O · bayesian · heterogeneous K operator. Observations are corrupted by measurement gaussian. Existence of the recovered 3D_hydraulic_conductivity 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 ~= 2000); density_dependent_flow_effects 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** → Spatial derivative → S · ade · solute transport → O · bayesian · heterogeneous K → **y** (detector). ``` y = `O.bayesian.heterogeneous_K` `S.ade.solute_transport` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.ade.solute_transport` | S · ade · solute transport operator | | `O.bayesian.heterogeneous_K` | O · bayesian · heterogeneous k operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Subsurface hydrology | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | 3D_hydraulic_conductivity | | Noise model | measurement_gaussian | | Integration axis | 3d_aquifer | | Difficulty delta | 5 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered 3D_hydraulic_conductivity 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 ~= 2000); density_dependent_flow_effects dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | hydraulic_head_RMSE_m | | Secondary | concentration_RMSE_mg_L | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `groundwater_monitoring_network` **Center point:** | Parameter | Unit | Value | |---|---|---| | N wells | — | 20 | | Log k variance | — | 2 | | Domain area km2 | — | 1 | | Contamination years | — | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N wells | — | 5 – 200 | | Log k variance | — | 0.5 – 6.0 | | Domain area km2 | — | 0.01 – 100 | | Contamination years | — | 1 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.1 hydraulic_head_RMSE_m | Metric | Range | |---|---| | Hydraulic head rmse m | 0.01 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **hydraulic_head_RMSE_m**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3dd2adc56394f89401e5d71e73c89bda9d70c6ed029a49795553cc24bebdf97e` - **Chain tx hash:** `0x0ab705cd87e01a2437568aec04784551a43e9458eae2570f61828c7ceaaf2433` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-425.md`, `L1-425.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-425.md` | Source of truth — edit this | Human or LLM | | `L1-425.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 `L1-425`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-425.md).
Regenerate L1-425.json so every field matches the Markdown.
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L2-425-001 Groundwater Contaminant Transport Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555239,
  "chain_hash": "0x3dd2adc56394f89401e5d71e73c89bda9d70c6ed029a49795553cc24bebdf97e",
  "chain_tx_hash": "0x0ab705cd87e01a2437568aec04784551a43e9458eae2570f61828c7ceaaf2433",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 100000.0,
    "metric": "hydraulic_head_RMSE_m",
    "type": "epsilon_fn"
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  "initiator_dataset": [
    {
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "hydraulic_head_RMSE_m",
    "regime": "Existence of the recovered 3D_hydraulic_conductivity 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 ~= 2000); density_dependent_flow_effects dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "concentration_RMSE_mg_L"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "3d_aquifer",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.space",
      "S.ade.solute_transport",
      "O.bayesian.heterogeneous_K"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "groundwater_monitoring_network",
    "solution_space": "3D_hydraulic_conductivity",
    "sub_domain": "Subsurface hydrology",
    "title": "Groundwater Contaminant Transport Inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "groundwater_monitoring_network"
    ],
    "allowed_omega_dimensions": [
      "N_wells",
      "domain_area_km2",
      "log_K_variance",
      "contamination_years"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.1 hydraulic_head_RMSE_m",
      "forward_operator": "groundwater_monitoring_network",
      "input_format": "measurement_only",
      "omega": {
        "N_wells": 20,
        "contamination_years": 20,
        "domain_area_km2": 1.0,
        "log_K_variance": 2.0
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "hydraulic_head_RMSE_m": [
        0.01,
        1.0
      ]
    },
    "omega_bounds": {
      "N_wells": [
        5,
        200
      ],
      "contamination_years": [
        1,
        100
      ],
      "domain_area_km2": [
        0.01,
        100
      ],
      "log_K_variance": [
        0.5,
        6.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Subsurface hydrology",
  "title": "Groundwater Contaminant Transport Inversion"
}

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