# 📐 L2 Spec — Phase Retrieval — Gerchberg-Saxton / hybrid input-output Mismatch-Only Spec
**ID:** `L2-247-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-247`](/artifact/l1/L1-247)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41553993
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 4096 |
| W | px | 64 – 4096 |
| Snr db | dB | 0 – 40 |
| Oversampling | — | 1.0 – 10.0 |
| Support error | — | 0.0 – 0.2 |
| Stagnation risk | — | 0.0 – 0.5 |
| Oversampling error | — | 0.0 – 0.2 |
## 2. Tolerance (ε)
**Type:** `fn`
```
17.0 + 2.0*log2(oversampling/1.0) + 0.25*SNR_dB - 12.0*support_error - 10.0*oversampling_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`046c451d78cf4cae681afae1062be11dade616ccc99cb4ab2a02ad6bf2095b12`
## 5. On-chain Registration
- **Chain hash:** `0x2705aa031c84c4f7eb83e2b5e483b9020777996ae3c0821ecd725f983276ad54`
- **Chain tx hash:** `0xa6192778c83b8a39cf89ee34ddebee95f83f48129a5ca2c08ac391f25b834461`
- **Chain block:** `41553993`
---
## File Mapping
This bundle consists of: `L2-247-001.md`, `L2-247-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-247-001.md` | Source of truth — edit this | Human or LLM |
| `L2-247-001.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 `L2-247-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._