# 📐 L2 Spec — APT Reconstruction Spec (hemispherical projection family)
**ID:** `L2-128-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-128`](/artifact/l1/L1-128)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.65 · **Delta tier:** 5
> **⛓ On-chain block:** 41554216
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| T k | — | 20 – 100 |
| Eta | — | 0.2 – 0.9 |
| R t nm | nm | 20 – 200 |
| N events | — | 10000.0 – 10000000000.0 |
| K species | — | 1 – 20 |
| Ranging ambiguity | — | 0.0 – 0.3 |
| Pile up correction | — | 0.0 – 0.2 |
| Detection efficiency | — | 0.2 – 0.9 |
| Multi phase evaporation | — | 0.0 – 0.3 |
| Local magnification error | — | 0.0 – 0.5 |
## 2. Tolerance (ε)
**Type:** `fn`
```
0.2 + 1.0 * local_magnification_error + 0.5 * multi_phase_evaporation + 0.3 * ranging_ambiguity + 0.5 * pile_up_correction
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.65 |
| Delta tier | 5 |
## 4. Fingerprint
`5a9ee9dc53a1c9a09085c0d8eb26fd73a7095df52eb832562cc8eae44a3f70bd`
## 5. On-chain Registration
- **Chain hash:** `0xa32bc46df0f538f2f452aa9a6cc64276dbdc72f1b3d23f9df45e8b92001d3862`
- **Chain tx hash:** `0x765b42bad27d64de5b570927c30ed90d3d0affd377df9dcbb88bb8f73a168553`
- **Chain block:** `41554216`
---
## File Mapping
This bundle consists of: `L2-128-001.md`, `L2-128-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-128-001.md` | Source of truth — edit this | Human or LLM |
| `L2-128-001.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 `L2-128-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._