# 📐  L2 Spec — Cable Equation (Dendrite Propagation) — Nominal + Mismatch Specs

**ID:** `L2-398-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-398`](/artifact/l1/L1-398)

> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.28 · **Delta tier:** 5
> **⛓ On-chain block:** 41555220

---

## 1. Domain Ω

**Type:** `range`

| Parameter | Unit | Range |
|---|---|---|
| Noise sigma mv | — | 0.01 – 2.0 |
| Cable length um | µm | 50 – 5000 |
| N recording sites | — | 1 – 20 |
| Lambda space constant um | µm | 50 – 1000 |

## 2. Tolerance (ε)

**Type:** `fn`

```
0.10 + 0.05 * (3 / N_recording_sites) ** 0.5
```

## 3. Difficulty

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

## 4. Fingerprint

`7e94924dac90f5296d90f7b76432d8753a70eac8d78c59c57ba8577ee4e4c980`

## 5. On-chain Registration

- **Chain hash:** `0x14bfee96747165d0f9f975b35b02eb72eee4aab6969956b5d6298ba1dd17cf7e`
- **Chain tx hash:** `0x573a7de9367a364189b1c624ec86a80a914f3a12bef781e853bb8f621fbe96d6`
- **Chain block:** `41555220`

---

## File Mapping

This bundle consists of: `L2-398-001.md`, `L2-398-001.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-398-001.md` | Source of truth — edit this | Human or LLM |
| `L2-398-001.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 `L2-398-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._