# 📐 L2 Spec — Robust PCA Entry-Corruption Spec (video background subtraction family)
**ID:** `L2-393-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-393`](/artifact/l1/L1-393)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.35 · **Delta tier:** 5
> **⛓ On-chain block:** 41555202
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| M | — | 50 – 10000 |
| N | — | 50 – 10000 |
| R | — | 1 – 500 |
| Mu 0 | — | 1.0 – 10.0 |
| Lambda | — | 0.1 – 10 |
| Sigma n | N | 0.0 – 0.1 |
| S fraction | — | 0.0 – 0.5 |
| Column corruption | — | 0.0 – 0.3 |
## 2. Tolerance (ε)
**Type:** `fn`
```
1e-4 * max(1, r * mu_0 / min(m,n)) * (1 + 10 * s_fraction) + 5 * sigma_n**2
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.35 |
| Delta tier | 5 |
## 4. Fingerprint
`37da4c9a23c91511b6896ccc3ad2f5bf30d97a449edfd70475c179a69c3aad41`
## 5. On-chain Registration
- **Chain hash:** `0x9663180421ed942ee5969c12c9e5cdf1285fc5bfbdfb4d80190e90aba6a5a7f5`
- **Chain tx hash:** `0x5e5cf783708fdbb9f9f686d77985dd4da630ef1f9e27287a36706607f0043835`
- **Chain block:** `41555202`
---
## File Mapping
This bundle consists of: `L2-393-001.md`, `L2-393-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-393-001.md` | Source of truth — edit this | Human or LLM |
| `L2-393-001.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 `L2-393-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._