# ⚛  L1 Principle — Creep Mechanics — high-temperature rate-dependent

**ID:** `L1-219` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Structural Mechanics — *Secondary/tertiary creep (Norton / Kachanov)*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** creep rate field
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554011

---

## 🧠 1. Introduction

**Creep Mechanics — high-temperature rate-dependent** is a **nonlinear inverse problem** whose unknown lives in **creep rate field** space, within the **Secondary/tertiary creep (Norton / Kachanov)** sub-domain of **Structural Mechanics**.

Measurements consist of mechanical vibrations or strain signals via a **extensometer dic** sensing mechanism.

The forward operator applies, in order: L · norton law operator; L · damage evolution operator; L · time integration operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · norton law → L · damage evolution → L · time integration → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.time_integration` `L.damage_evolution` `L.norton_law` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.norton_law` | L · norton law operator |
| `L.damage_evolution` | L · damage evolution operator |
| `L.time_integration` | L · time integration operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Structural Mechanics |
| Sub domain | Secondary/tertiary creep (Norton / Kachanov) |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | creep_rate_field |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `creep` · **Forward operator:** `creep_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 873 |
| N dof | — | 10000 |
| Snr db | dB | 30 |
| A error | — | 0 |
| N times | — | 500 |
| Q error | — | 0 |
| N error | — | 0 |
| Damage param error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 273 – 2000 |
| N dof | — | 100 – 1000000 |
| Snr db | dB | 0 – 40 |
| A error | — | 0.0 – 0.2 |
| N times | — | 10 – 100000 |
| Q error | — | 0.0 – 0.1 |
| N error | — | 0.0 – 0.1 |
| Damage param error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 20.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xffe5847e1b935197570988958a615aad35b51caa9518573ba334cdd5f1cb69ff`
- **Chain tx hash:** `0xbf9fc75c8cdf439d4fb6dfa566fbbd17916904e9edea708756bd00dc03ea1d2b`
- **Chain block:** `41554011`

---

## File Mapping

This bundle consists of: `L1-219.md`, `L1-219.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-219.md` | Source of truth — edit this | Human or LLM |
| `L1-219.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 `L1-219`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._