L1 ⚛ L1-423 ⊙ Testnet

Contaminant Source Identification

Environmental Science · Inverse dispersion

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⬇ L1-423.md

# ⚛ L1 Principle — Contaminant Source Identification **ID:** `L1-423` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Inverse dispersion* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** source location strength time > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **Contaminant Source Identification** is a **nonlinear inverse problem** whose unknown lives in **source location strength time** space, within the **Inverse dispersion** sub-domain of **Environmental Science**. Measurements consist of N/A via a **environmental concentration inversion** sensing mechanism. The forward operator applies, in order: a fixed-point or gradient iteration on the unknown; O · bayesian · mcmc source operator; S · green function · transport operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered source_location_strength_time 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); transport_model_uncertainty 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** → O · bayesian · mcmc source → S · green function · transport → **y** (detector). ``` y = `S.green_function.transport` `O.bayesian.mcmc_source` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `O.bayesian.mcmc_source` | O · bayesian · mcmc source operator | | `S.green_function.transport` | S · green function · transport operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Inverse dispersion | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | source_location_strength_time | | Noise model | lognormal | | Integration axis | spatiotemporal_domain | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered source_location_strength_time 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); transport_model_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | source_location_error_m | | Secondary | emission_rate_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `environmental_concentration_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | N sensors | — | 15 | | Domain radius km | km | 5 | | N time observations | — | 50 | | Transport uncertainty percent | — | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N sensors | — | 3 – 100 | | Domain radius km | km | 0.1 – 100.0 | | N time observations | — | 5 – 500 | | Transport uncertainty percent | — | 5 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 100 source_location_error_m | Metric | Range | |---|---| | Source location error m | 10 – 1000 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **source_location_error_m**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x699733d75f28edaad30696d5fa593a58031a18fbf2754f14d3fa268a7992676d` - **Chain tx hash:** `0x22d1b301773ce69cb251e2681a83c2995f332f086496252480f6ac4c13de3254` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-423.md`, `L1-423.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-423.md` | Source of truth — edit this | Human or LLM | | `L1-423.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 `L1-423`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-423.md).
Regenerate L1-423.json so every field matches the Markdown.
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L2-423-001 Contaminant Source Identification — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555239,
  "chain_hash": "0x699733d75f28edaad30696d5fa593a58031a18fbf2754f14d3fa268a7992676d",
  "chain_tx_hash": "0x22d1b301773ce69cb251e2681a83c2995f332f086496252480f6ac4c13de3254",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000.0,
    "metric": "source_location_error_m",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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    "regime": "Existence of the recovered source_location_strength_time 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); transport_model_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.",
    "secondary": "emission_rate_RMSE_percent"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "spatiotemporal_domain",
    "noise_model": "lognormal",
    "primitives": [
      "O.iter",
      "O.bayesian.mcmc_source",
      "S.green_function.transport"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "environmental_concentration_inversion",
    "solution_space": "source_location_strength_time",
    "sub_domain": "Inverse dispersion",
    "title": "Contaminant Source Identification"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "environmental_concentration_inversion"
    ],
    "allowed_omega_dimensions": [
      "N_sensors",
      "domain_radius_km",
      "transport_uncertainty_percent",
      "N_time_observations"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "100 source_location_error_m",
      "forward_operator": "environmental_concentration_inversion",
      "input_format": "measurement_only",
      "omega": {
        "N_sensors": 15,
        "N_time_observations": 50,
        "domain_radius_km": 5.0,
        "transport_uncertainty_percent": 20
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "source_location_error_m": [
        10,
        1000
      ]
    },
    "omega_bounds": {
      "N_sensors": [
        3,
        100
      ],
      "N_time_observations": [
        5,
        500
      ],
      "domain_radius_km": [
        0.1,
        100.0
      ],
      "transport_uncertainty_percent": [
        5,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Inverse dispersion",
  "title": "Contaminant Source Identification"
}

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