# 📐 L2 Spec — Matrix Completion Uniform-Sampling Spec (MovieLens family)
**ID:** `L2-392-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-392`](/artifact/l1/L1-392)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.5 · **Delta tier:** 5
> **⛓ On-chain block:** 41555202
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| M | — | 50 – 10000 |
| N | — | 50 – 10000 |
| P | — | 0.05 – 0.9 |
| R | — | 1 – 500 |
| Mu 0 | — | 1.0 – 10.0 |
| Sigma n | N | 0.0 – 0.1 |
| Sampling bias | — | 0.0 – 1.0 |
## 2. Tolerance (ε)
**Type:** `fn`
```
1e-3 * max(1, mu_0**2 * r * (m+n) / (p * m * n)) + 10 * sigma_n**2 + 2 * sampling_bias
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.5 |
| Delta tier | 5 |
## 4. Fingerprint
`a25ccedbc8bfead1744a614f153176643fd38868fd72c17c75adba675142c0c2`
## 5. On-chain Registration
- **Chain hash:** `0x70a24cc71655a08e27829d38524c26e304f8ab6e916a296cf343041b2dea4b28`
- **Chain tx hash:** `0x68a37419c6d7dc3ad829378276ac3d8e00bf7b73fa490f5f3889b0fcb15e312d`
- **Chain block:** `41555202`
---
## File Mapping
This bundle consists of: `L2-392-001.md`, `L2-392-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-392-001.md` | Source of truth — edit this | Human or LLM |
| `L2-392-001.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 `L2-392-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._