# 📐 L2 Spec — Shell Theory — curved thin-structure mechanics Mismatch-Only Spec
**ID:** `L2-212-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-212`](/artifact/l1/L1-212)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554013
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| N dof | — | 100 – 1000000 |
| Snr db | dB | 0 – 40 |
| Bc error | — | 0.0 – 0.2 |
| N sensors | — | 4 – 4096 |
| Material error | — | 0.0 – 0.1 |
| Curvature error | — | 0.0 – 0.05 |
| Thickness error | — | 0.0 – 0.05 |
## 2. Tolerance (ε)
**Type:** `fn`
```
17.5 + 0.3*SNR_dB - 30.0*curvature_error - 40.0*thickness_error - 20.0*material_error - 10.0*BC_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`6b5c47d563ae35226c97d3098000b397c1abddcddb4a6848ac3740994df64ce8`
## 5. On-chain Registration
- **Chain hash:** `0x12f30d54bd18a1d8914968e645ebc042f30a5e045f55a527f97fcabf0be09831`
- **Chain tx hash:** `0x04e748e5b1847de24d4658cc38db3c878dc001dc4a4a451afebd47a89d6a9563`
- **Chain block:** `41554013`
---
## File Mapping
This bundle consists of: `L2-212-001.md`, `L2-212-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-212-001.md` | Source of truth — edit this | Human or LLM |
| `L2-212-001.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 `L2-212-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._