# ⚛  L1 Principle — Sediment Transport Inversion

**ID:** `L1-422` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Environmental Science — *Geomorphology*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** sediment flux parameter vector
> **📡 Carrier:** N/A · **🌫 Noise:** lognormal
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555239

---

## 🧠 1. Introduction

**Sediment Transport Inversion** is a **parameter-estimation problem** whose unknown lives in **sediment flux parameter vector** space, within the **Geomorphology** sub-domain of **Environmental Science**.

Measurements consist of N/A via a **bedload suspended measurement** sensing mechanism.

The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · vanrijn · suspended load operator; O · chi2 · bedload flux operator.

Observations are corrupted by log-normal multiplicative noise. Existence of the recovered sediment_flux_parameter_vector 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 ~= 40); armoring_effect 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** → Pointwise nonlinearity → S · vanrijn · suspended load → O · chi2 · bedload flux → **y** (detector).

```
y = `O.chi2.bedload_flux` `S.vanrijn.suspended_load` f(·) x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `N.pointwise` | Applies a smooth nonlinear function element-wise |
| `S.vanrijn.suspended_load` | S · vanrijn · suspended load operator |
| `O.chi2.bedload_flux` | O · chi2 · bedload flux operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Environmental Science |
| Sub domain | Geomorphology |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | sediment_flux_parameter_vector |
| Noise model | lognormal |
| Integration axis | channel_cross_section |
| Difficulty delta | 3 |
| L dag | 2.8 |

## 📡 4. Measurement Model

Existence of the recovered sediment_flux_parameter_vector 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 ~= 40); armoring_effect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | bedload_flux_RMSE_log |
| Secondary | sediment_rating_curve_RMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `bedload_suspended_measurement`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| D50 mm | mm | 2 |
| N measurements | — | 100 |
| Discharge m3 s | s | 500 |
| Critical shields tau*c | — | 0.047 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| D50 mm | mm | 0.1 – 100.0 |
| N measurements | — | 10 – 1000 |
| Discharge m3 s | s | 1 – 100000 |
| Critical shields tau*c | — | 0.02 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.5 bedload_flux_RMSE_log

| Metric | Range |
|---|---|
| Bedload flux rmse log | 0.1 – 2.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **bedload_flux_RMSE_log**, with κ = `1000` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x64e4ec96dd87f1fe73dab04733c2fcc411af3f88d419c32d83a8bf71d50bcb4c`
- **Chain tx hash:** `0x48e68af5737c0ee07a49eb882024e555e613f4998b11466e99a895d1f28d6e99`
- **Chain block:** `41555239`

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## File Mapping

This bundle consists of: `L1-422.md`, `L1-422.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-422.md` | Source of truth — edit this | Human or LLM |
| `L1-422.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 `L1-422`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._