# 📐 L2 Spec — Acoustic Beamforming — DOA & imaging from array Mismatch-Only Spec
**ID:** `L2-265-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-265`](/artifact/l1/L1-265)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554052
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| N mic | — | 4 – 256 |
| Snr db | dB | -10 – 40 |
| N sources | — | 1 – 8 |
| N snapshots | — | 16 – 8192 |
| Sensor pos error | — | 0.0 – 0.1 |
| Element gain error | — | 0.0 – 0.2 |
| Element phase error | — | 0.0 – 0.3 |
## 2. Tolerance (ε)
**Type:** `fn`
```
3.0 - 0.2*SNR_dB + 30.0*sensor_pos_error + 10.0*element_phase_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`279fcc2c93d292748839817a3c647b6542cc92e28641452bbdb8b3d5ce4d5e99`
## 5. On-chain Registration
- **Chain hash:** `0xcc24e29a97081a8d7a1057f4d2c2f619c10f650788838ad1f82e88d11183ec29`
- **Chain tx hash:** `0xa7aca7532a2a23db73a3d2c327fe18b471af2f44cc578cc22b4bc0db0a5b8ca9`
- **Chain block:** `41554052`
---
## File Mapping
This bundle consists of: `L2-265-001.md`, `L2-265-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-265-001.md` | Source of truth — edit this | Human or LLM |
| `L2-265-001.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 `L2-265-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._