L1 ⚛ L1-471 ⊙ Testnet

Satellite Gravity Gradiometry (GOCE)

Geodesy · Earth gravity field

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⬇ L1-471.md

# ⚛ L1 Principle — Satellite Gravity Gradiometry (GOCE) **ID:** `L1-471` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Earth gravity field* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** spherical harmonic gravity > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555299 --- ## 🧠 1. Introduction **Satellite Gravity Gradiometry (GOCE)** is a **linear inverse problem** whose unknown lives in **spherical harmonic gravity** space, within the **Earth gravity field** sub-domain of **Geodesy**. Measurements consist of N/A via a **gravity gradient tensor measurement** sensing mechanism. The forward operator applies, in order: S · gravity · gradient tensor operator; operator inherits structure from a graph (mesh, network); O · tikhonov · regularization operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered spherical_harmonic_gravity 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 ~= 5000); calibration_bias_mE dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · gravity · gradient tensor → Structured graph operator → O · tikhonov · regularization → **y** (detector). ``` y = `O.tikhonov.regularization` G `S.gravity.gradient_tensor` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.gravity.gradient_tensor` | S · gravity · gradient tensor operator | | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `O.tikhonov.regularization` | O · tikhonov · regularization operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Earth gravity field | | Carrier | N/A | | Problem class | linear_inverse | | Solution space | spherical_harmonic_gravity | | Noise model | gaussian | | Integration axis | orbital_track | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered spherical_harmonic_gravity 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 ~= 5000); calibration_bias_mE dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | geoid_height_RMSE_mm | | Secondary | gravity_anomaly_RMSE_mGal | ## 📏 5. Operating Range (Ω) **Center problem class:** `linear_inverse` · **Forward operator:** `gravity_gradient_tensor_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N arc days | — | 365 | | N max degree | — | 200 | | Noise e sqrt hz | Hz | 5 | | Orbit altitude km | km | 255 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N arc days | — | 100 – 1825 | | N max degree | — | 50 – 300 | | Noise e sqrt hz | Hz | 1.0 – 50.0 | | Orbit altitude km | km | 200 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.0 geoid_height_RMSE_mm | Metric | Range | |---|---| | Geoid height rmse mm | 0.1 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **geoid_height_RMSE_mm**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8c81d763f3d6b1560897c7d4ed08649d1d7b2673be6d87c21964b499eba576a3` - **Chain tx hash:** `0xf9f2401e862e869736323f98155c7caf800a5120f81b5c4ef3a4b33266e45b2b` - **Chain block:** `41555299` --- ## File Mapping This bundle consists of: `L1-471.md`, `L1-471.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-471.md` | Source of truth — edit this | Human or LLM | | `L1-471.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 `L1-471`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-471.md).
Regenerate L1-471.json so every field matches the Markdown.
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L2-471-001 Satellite Gravity Gradiometry (GOCE) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555299,
  "chain_hash": "0x8c81d763f3d6b1560897c7d4ed08649d1d7b2673be6d87c21964b499eba576a3",
  "chain_tx_hash": "0xf9f2401e862e869736323f98155c7caf800a5120f81b5c4ef3a4b33266e45b2b",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 100000.0,
    "metric": "geoid_height_RMSE_mm",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "geoid_height_RMSE_mm",
    "regime": "Existence of the recovered spherical_harmonic_gravity 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 ~= 5000); calibration_bias_mE dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "gravity_anomaly_RMSE_mGal"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Geodesy",
    "integration_axis": "orbital_track",
    "noise_model": "gaussian",
    "primitives": [
      "S.gravity.gradient_tensor",
      "G.structured",
      "O.tikhonov.regularization"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "gravity_gradient_tensor_measurement",
    "solution_space": "spherical_harmonic_gravity",
    "sub_domain": "Earth gravity field",
    "title": "Satellite Gravity Gradiometry (GOCE)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "gravity_gradient_tensor_measurement"
    ],
    "allowed_omega_dimensions": [
      "N_max_degree",
      "orbit_altitude_km",
      "noise_E_sqrt_Hz",
      "N_arc_days"
    ],
    "allowed_problem_classes": [
      "linear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.0 geoid_height_RMSE_mm",
      "forward_operator": "gravity_gradient_tensor_measurement",
      "input_format": "measurement_only",
      "omega": {
        "N_arc_days": 365,
        "N_max_degree": 200,
        "noise_E_sqrt_Hz": 5.0,
        "orbit_altitude_km": 255
      },
      "problem_class": "linear_inverse"
    },
    "epsilon_bounds": {
      "geoid_height_RMSE_mm": [
        0.1,
        50.0
      ]
    },
    "omega_bounds": {
      "N_arc_days": [
        100,
        1825
      ],
      "N_max_degree": [
        50,
        300
      ],
      "noise_E_sqrt_Hz": [
        1.0,
        50.0
      ],
      "orbit_altitude_km": [
        200,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Earth gravity field",
  "title": "Satellite Gravity Gradiometry (GOCE)"
}

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