# 📐 L2 Spec — Transient Heat Conduction — inverse heat conduction (IHCP) Mismatch-Only Spec
**ID:** `L2-195-001` · **Status:** ⊙ Testnet (genesis catalog)
**Parents:** ⬆ Principle [`L1-195`](/artifact/l1/L1-195)
> **🎯 Tolerance (ε):** expression
> **⚖ Difficulty score:** 0.48 · **Delta tier:** 5
> **⛓ On-chain block:** 41554036
---
## 1. Domain Ω
**Type:** `range`
| Parameter | Unit | Range |
|---|---|---|
| H | px | 16 – 512 |
| W | px | 16 – 512 |
| Z | — | 8 – 256 |
| Fs hz | Hz | 0.1 – 1000 |
| Snr db | dB | 0 – 40 |
| K error | — | 0.0 – 0.1 |
| Bc error | — | 0.0 – 0.5 |
| N samples | — | 20 – 10000 |
| N sensors | — | 4 – 256 |
| Rho cp error | — | 0.0 – 0.1 |
| Sensor pos error | — | 0.0 – 0.02 |
## 2. Tolerance (ε)
**Type:** `fn`
```
18.0 + 2.0*log2(N_sensors/4) + 0.3*SNR_dB - 50.0*k_error - 10.0*sensor_pos_error - 5.0*bc_error
```
## 3. Difficulty
| Property | Value |
|---|---|
| Difficulty score | 0.48 |
| Delta tier | 5 |
## 4. Fingerprint
`2a421e0e6f806c7e5de041beaf9963a8ad30f42ed001454f9acb8af1df047edc`
## 5. On-chain Registration
- **Chain hash:** `0xff60d6d27cb36295781c99d381294cd1e63c99dddd43ca190c6cf97b7183725d`
- **Chain tx hash:** `0xcd16e25c9546545b7b52552d24a5d715fb32c1570c54dd0e68b7c76aa17a2ae5`
- **Chain block:** `41554036`
---
## File Mapping
This bundle consists of: `L2-195-001.md`, `L2-195-001.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L2-195-001.md` | Source of truth — edit this | Human or LLM |
| `L2-195-001.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 `L2-195-001`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._