# ⚛  L1 Principle — Tidal Analysis — harmonic tidal constituent extraction

**ID:** `L1-292` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Harmonic tidal analysis from tide gauge*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** tidal harmonic amps phases
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554066

---

## 🧠 1. Introduction

**Tidal Analysis — harmonic tidal constituent extraction** is a **linear inverse problem** whose unknown lives in **tidal harmonic amps phases** space, within the **Harmonic tidal analysis from tide gauge** sub-domain of **Geophysics**.

Measurements consist of mechanical vibrations or strain signals via a **tide gauge** sensing mechanism.

The forward operator applies, in order: L · fourier harmonic operator; L · nodal correction operator; L · least squares operator; integration over a band of frequencies.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · fourier harmonic → L · nodal correction → L · least squares → Frequency integration → **y** (detector).

```
y = ∫dω `L.least_squares` `L.nodal_correction` `L.fourier_harmonic` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.fourier_harmonic` | L · fourier harmonic operator |
| `L.nodal_correction` | L · nodal correction operator |
| `L.least_squares` | L · least squares operator |
| `int.frequency` | Integration over a band of frequencies |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Harmonic tidal analysis from tide gauge |
| Carrier | mechanical |
| Problem class | linear_inverse |
| Solution space | tidal_harmonic_amps_phases |
| Noise model | gaussian |
| Integration axis | frequency |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `tide_harmonic` · **Forward operator:** `tide_harmonic_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 40 |
| N samples | — | 17520 |
| Nodal error | — | 0 |
| N constituents | — | 37 |
| Residual surge | — | 0 |
| Shallow water error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 10 – 60 |
| N samples | — | 720 – 525600 |
| Nodal error | — | 0.0 – 0.05 |
| N constituents | — | 5 – 200 |
| Residual surge | — | 0.0 – 0.3 |
| Shallow water error | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 28.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x34bdda3d752390eb4e2b7a58cf4b031478f9bb3ed955e18b83281c7e4abb031d`
- **Chain tx hash:** `0x0d05c7a7d18078778b7e3e5738b5574997dc2375524c67d6ecfb49932d2c68c9`
- **Chain block:** `41554066`

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## File Mapping

This bundle consists of: `L1-292.md`, `L1-292.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-292.md` | Source of truth — edit this | Human or LLM |
| `L1-292.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 `L1-292`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._