# 📐  L2 Spec — Markowitz Mean-Variance Portfolio Optimization — Nominal + Mismatch Specs

**ID:** `L2-444-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-444`](/artifact/l1/L1-444)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.28 · **Delta tier:** 5
> **⛓ On-chain block:** 41555263

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| N assets | — | 5 – 500 |
| T lookback days | — | 63 – 2520 |
| Risk aversion lambda | — | 0.1 – 10.0 |
| Estimation error sigma mu | — | 0.001 – 0.05 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.4 + 0.2 * sqrt(T_lookback_days / 252)
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.28 |
| Delta tier | 5 |

## 4. Fingerprint

`211e3b98ddf0dbe2dac8153d4b0fcaabfb52b31ab1f3749ad8ff6ed900c712fe`

## 5. On-chain Registration

- **Chain hash:** `0xc6f70de5bc6f9c1e35640d7b47f096a087744e1f3185cf08c4d082a0c513de6c`
- **Chain tx hash:** `0xf94ac128f07c502dd4930a63a44cf26a14d9f66e931dedf589222153e593bedb`
- **Chain block:** `41555263`

---

## File Mapping

This bundle consists of: `L2-444-001.md`, `L2-444-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-444-001.md` | Source of truth — edit this | Human or LLM |
| `L2-444-001.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 `L2-444-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._