# 📐 L2 Spec — Gaussian Matrix Sensing Mismatch-Only Spec
**ID:** `L2-028-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-028`](/artifact/l1/L1-028)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.55 · **Delta tier:** 5
> **⛓ On-chain block:** 41547812
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| N1 | — | 32 – 2048 |
| N2 | — | 32 – 2048 |
| Rank r | — | 1 – 50 |
| Noise level | — | 0.001 – 0.1 |
| M over minmn | — | 2 – 30 |
| Rank misspec | — | 0 – 10 |
| Measurement noise tail | — | 0.0 – 0.2 |
## 2. Tolerance (ε)
**Type:** `fn`
```
0.10 - 0.02 * log2(m_over_minmn / 2) + 0.02 * log10(noise_level / 0.001)
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.55 |
| Delta tier | 5 |
## 4. Fingerprint
`9d9fc4db824c3d0adf86b0aca883f3cce211987276977abf650b9c87c5778119`
## 5. On-chain Registration
- **Chain hash:** `0xed5b4a6112d185094ce22fe213f20784131ee4500929d28acc4d2b9413a1bb0c`
- **Chain tx hash:** `0x120cea181027fc3b31bea82535adf651c730b9f673796b8e534ff2ad01d525f7`
- **Chain block:** `41547812`
---
## File Mapping
This bundle consists of: `L2-028-001.md`, `L2-028-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-028-001.md` | Source of truth — edit this | Human or LLM |
| `L2-028-001.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 `L2-028-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._