# ⚛  L1 Principle — Glacial Isostatic Adjustment (GIA) — post-glacial rebound

**ID:** `L1-287` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Viscoelastic Earth + ice-load history*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** vertical uplift and viscosity
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554065

---

## 🧠 1. Introduction

**Glacial Isostatic Adjustment (GIA) — post-glacial rebound** is a **nonlinear inverse problem** whose unknown lives in **vertical uplift and viscosity** space, within the **Viscoelastic Earth + ice-load history** sub-domain of **Geophysics**.

Measurements consist of mechanical vibrations or strain signals via a **gps sea level** sensing mechanism.

The forward operator applies, in order: L · load history operator; L · viscoelastic response operator; L · sea level eqn operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · load history → L · viscoelastic response → L · sea level eqn → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.sea_level_eqn` `L.viscoelastic_response` `L.load_history` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.load_history` | L · load history operator |
| `L.viscoelastic_response` | L · viscoelastic response operator |
| `L.sea_level_eqn` | L · sea level eqn operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Viscoelastic Earth + ice-load history |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | vertical_uplift_and_viscosity |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | uplift_rel_error_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `gia` · **Forward operator:** `gia_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N gps | — | 100 |
| Snr db | dB | 25 |
| N layers | — | 20 |
| N load history | — | 10000 |
| Ice history error | — | 0.1 |
| Mantle viscosity error | — | 0.1 |
| Lithosphere thickness error | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N gps | — | 10 – 10000 |
| Snr db | dB | 0 – 40 |
| N layers | — | 5 – 1000 |
| N load history | — | 100 – 1000000 |
| Ice history error | — | 0.0 – 0.3 |
| Mantle viscosity error | — | 0.0 – 0.5 |
| Lithosphere thickness error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 2.0

| Metric | Range |
|---|---|
| Uplift rel | 0.2 – 20.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **uplift_rel_error_percent**, with κ = `560` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x863057f22fae9ae7cb15c4def70a498df0d05d5d144f09d1310bb3dc61251aed`
- **Chain tx hash:** `0x30d68e14816d0e3f12c9d56afe03ae38d38062c2ffc32ad05b3d46061ac6ba92`
- **Chain block:** `41554065`

---

## File Mapping

This bundle consists of: `L1-287.md`, `L1-287.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-287.md` | Source of truth — edit this | Human or LLM |
| `L1-287.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 `L1-287`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._