# ⚛  L1 Principle — Fault-Tolerant Thresholds & Surface-Code Decoding

**ID:** `L1-921` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Quantum Computing — *Quantum Error Correction*

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## 🧠 1. Introduction

**Fault-Tolerant Thresholds & Surface-Code Decoding** is a **inverse problem**, within the **Quantum Error Correction** sub-domain of **Quantum Computing**.

## ⚙ 2. Forward Model

```
Logical error rate p_L of a distance-d surface code under a decoder: p_L ≈ A·(p/p_th)^{⌊(d+1)/2⌋}; below threshold p<p_th, p_L falls exponentially with d.
```

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Quantum Computing |
| Sub domain | Quantum Error Correction |

## 📡 4. Measurement Model

| Metric | Value |
|---|---|
| Metric | logical_error_rate |

## ⚖ 6. Hardness Function

Hardness scales as **`grand_challenge`** on **logical_error_rate**.

## 💾 7. Reference Dataset

- **Surface-code syndrome-measurement corpus** · weight 0.6 · IPFS _(not pinned yet)_
- **Repetition-code error chains** · weight 0.4 · IPFS _(not pinned yet)_

**Staked PWM:** 5000.0

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## File Mapping

This bundle consists of: `L1-921.md`, `L1-921.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-921.md` | Source of truth — edit this | Human or LLM |
| `L1-921.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 `L1-921`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._