L1 ⚛ L1-424 ⊙ Testnet

Carbon Cycle Biogeochemical Inversion

Environmental Science · Carbon cycle

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⬇ L1-424.md

# ⚛ L1 Principle — Carbon Cycle Biogeochemical Inversion **ID:** `L1-424` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Carbon cycle* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** NEE flux map > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **Carbon Cycle Biogeochemical Inversion** is a **linear inverse problem** whose unknown lives in **NEE flux map** space, within the **Carbon cycle** sub-domain of **Environmental Science**. Measurements consist of N/A via a **atmospheric CO2 inversion** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; O · bayesian · flux inversion operator; S · prior · biosphere model operator. Observations are corrupted by observation gaussian. Existence of the recovered NEE_flux_map 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); transport_model_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → O · bayesian · flux inversion → S · prior · biosphere model → **y** (detector). ``` y = `S.prior.biosphere_model` `O.bayesian.flux_inversion` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `O.bayesian.flux_inversion` | O · bayesian · flux inversion operator | | `S.prior.biosphere_model` | S · prior · biosphere model operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Carbon cycle | | Carrier | N/A | | Problem class | linear_inverse | | Solution space | NEE_flux_map | | Noise model | observation_gaussian | | Integration axis | global_atmosphere_land_ocean | | Difficulty delta | 5 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered NEE_flux_map 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); transport_model_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | global_NEE_uncertainty_GtC_yr | | Secondary | regional_flux_RMSE_GtC_yr | ## 📏 5. Operating Range (Ω) **Center problem class:** `linear_inverse` · **Forward operator:** `atmospheric_CO2_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | N flux regions | — | 22 | | N surface stations | — | 100 | | Prior uncertainty gtc yr | — | 1 | | Satellite coverage percent | — | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N flux regions | — | 11 – 100 | | N surface stations | — | 10 – 300 | | Prior uncertainty gtc yr | — | 0.1 – 5.0 | | Satellite coverage percent | — | 0 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 global_NEE_uncertainty_GtC_yr | Metric | Range | |---|---| | Global nee uncertainty gtc yr | 0.1 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **global_NEE_uncertainty_GtC_yr**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb449860f3dfd465ee0960a622f14af2a8a647ff443f04cc61139dae3c126ea46` - **Chain tx hash:** `0x8469da3bb1ffa075fd7a1dc7d6f060aee338ce578a452415008be885c5f749a2` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-424.md`, `L1-424.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-424.md` | Source of truth — edit this | Human or LLM | | `L1-424.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 `L1-424`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-424.md).
Regenerate L1-424.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-424-001 Carbon Cycle Biogeochemical Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_hash": "0xb449860f3dfd465ee0960a622f14af2a8a647ff443f04cc61139dae3c126ea46",
  "chain_tx_hash": "0x8469da3bb1ffa075fd7a1dc7d6f060aee338ce578a452415008be885c5f749a2",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 100000.0,
    "metric": "global_NEE_uncertainty_GtC_yr",
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    "regime": "Existence of the recovered NEE_flux_map 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); transport_model_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "regional_flux_RMSE_GtC_yr"
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  "physics_fingerprint": {
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    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Environmental Science",
    "integration_axis": "global_atmosphere_land_ocean",
    "noise_model": "observation_gaussian",
    "primitives": [
      "D.space",
      "O.bayesian.flux_inversion",
      "S.prior.biosphere_model"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "atmospheric_CO2_inversion",
    "solution_space": "NEE_flux_map",
    "sub_domain": "Carbon cycle",
    "title": "Carbon Cycle Biogeochemical Inversion"
  },
  "size_tiers": {
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      "atmospheric_CO2_inversion"
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    "allowed_omega_dimensions": [
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      "N_flux_regions",
      "satellite_coverage_percent",
      "prior_uncertainty_GtC_yr"
    ],
    "allowed_problem_classes": [
      "linear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.5 global_NEE_uncertainty_GtC_yr",
      "forward_operator": "atmospheric_CO2_inversion",
      "input_format": "measurement_only",
      "omega": {
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        "N_surface_stations": 100,
        "prior_uncertainty_GtC_yr": 1.0,
        "satellite_coverage_percent": 50
      },
      "problem_class": "linear_inverse"
    },
    "epsilon_bounds": {
      "global_NEE_uncertainty_GtC_yr": [
        0.1,
        3.0
      ]
    },
    "omega_bounds": {
      "N_flux_regions": [
        11,
        100
      ],
      "N_surface_stations": [
        10,
        300
      ],
      "prior_uncertainty_GtC_yr": [
        0.1,
        5.0
      ],
      "satellite_coverage_percent": [
        0,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Carbon cycle",
  "title": "Carbon Cycle Biogeochemical Inversion"
}

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