# 📐  L2 Spec — Modal Analysis — natural frequencies and mode shapes Mismatch-Only Spec

**ID:** `L2-213-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-213`](/artifact/l1/L1-213)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554014

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N dof | — | 100 – 500000 |
| Snr db | dB | 0 – 40 |
| N modes | — | 3 – 500 |
| Bc error | — | 0.0 – 0.2 |
| N sensors | — | 2 – 256 |
| Mass error | — | 0.0 – 0.1 |
| Stiffness error | — | 0.0 – 0.1 |

## 2. Tolerance (ε)

**Type:** `fn`

```
1.0 + 50.0*stiffness_error + 50.0*mass_error + 10.0*bc_error - 0.02*SNR_dB
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |

## 4. Fingerprint

`3768d7de577cff2c393919aa94a6f7945de85e7a7ff1df4b02397b28af5d8c78`

## 5. On-chain Registration

- **Chain hash:** `0xe98a7847d7921160937118a9ae2cdd902c16ee19f9b4ccf544af4b96a145ece8`
- **Chain tx hash:** `0x09d18781e3969cdd628e53114c5f3168988bc4281eae1eb336b8c9a3c76ce5ec`
- **Chain block:** `41554014`

---

## File Mapping

This bundle consists of: `L2-213-001.md`, `L2-213-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-213-001.md` | Source of truth — edit this | Human or LLM |
| `L2-213-001.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 `L2-213-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._