# 📐 L2 Spec — Sparse Signal Recovery Synthesis-Model Spec (overcomplete dictionary)
**ID:** `L2-391-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-391`](/artifact/l1/L1-391)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.22 · **Delta tier:** 5
> **⛓ On-chain block:** 41555201
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| M | — | 32 – 16384 |
| N | — | 128 – 16384 |
| K | — | 1 – 2000 |
| Mu | — | 0.01 – 0.8 |
| Sigma n | N | 0.0 – 0.1 |
| Off grid | — | 0.0 – 1.0 |
| Basis mismatch | — | 0.0 – 0.5 |
## 2. Tolerance (ε)
**Type:** `fn`
```
2e-3 * max(1, k*mu/sqrt(M)) * (1 + 5*basis_mismatch) + 10*sigma_n**2
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.22 |
| Delta tier | 5 |
## 4. Fingerprint
`aae3c7885da699774825cfdd724568265f674ab602e94a0518bbb52e563071d8`
## 5. On-chain Registration
- **Chain hash:** `0x435bd5bc3693d9defe4c2b2a73d6d11fb595ab1697c349ffff38e41216e923ab`
- **Chain tx hash:** `0x9d0c06f02de1794729b012d9f94611fe252ec2c84a26b1e8a9f8b3ae9f6dcf2a`
- **Chain block:** `41555201`
---
## File Mapping
This bundle consists of: `L2-391-001.md`, `L2-391-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-391-001.md` | Source of truth — edit this | Human or LLM |
| `L2-391-001.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 `L2-391-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._