# ⚛  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._