# 📐  L2 Spec — Channel Estimation OFDM/MIMO Spec (5G NR pilot family)

**ID:** `L2-389-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-389`](/artifact/l1/L1-389)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.5 · **Delta tier:** 5
> **⛓ On-chain block:** 41555201

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| K | — | 1 – 64 |
| Nr | — | 1 – 128 |
| Nt | — | 1 – 64 |
| L ch | — | 2 – 256 |
| Snr db | dB | -5 – 30 |
| Cfo hz | Hz | 0 – 500 |
| F d hz | Hz | 0 – 1000 |
| Alpha p | — | 0.02 – 0.5 |
| Doppler error | — | 0.0 – 100 |
| Phase noise rms | — | 0.0 – 0.1 |

## 2. Tolerance (ε)

**Type:** `fn`

```
1e-2 * max(1, k / (alpha_p * L_ch)) * 10**(-SNR_dB/10) + 0.5 * (f_d_Hz/1000) + 0.2 * phase_noise_rms
```

## 3. Difficulty

| Property | Value |
|---|---|
| Difficulty score | 0.5 |
| Delta tier | 5 |

## 4. Fingerprint

`04150b2f68465010897c7356217481cdddccffcd0e4f9d59a95366d93edf670f`

## 5. On-chain Registration

- **Chain hash:** `0x974ed055021ec2179497b408a5d6ee56f8e4fcbc075013f80bf6c2c9d3d1ee67`
- **Chain tx hash:** `0x4d5b0982ea9a654831a4806f6c84ddde53256face6b6d8e44897b81431b02cb8`
- **Chain block:** `41555201`

---

## File Mapping

This bundle consists of: `L2-389-001.md`, `L2-389-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-389-001.md` | Source of truth — edit this | Human or LLM |
| `L2-389-001.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 `L2-389-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._